58:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Números reales y funciones:@0.073089:0.043661:0.318030:0.043661:0.318030:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición.:@0.293660:0.231541:0.379051:0.231541:0.379051:0.214594:0.293660:0.214594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Sean  ,  ,   tres conjuntos no vacíos cualesquiera,   una función de   en  ,   :@0.378941:0.231541:0.930901:0.231541:0.930901:0.215828:0.378941:0.215828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.421830:0.231541:0.464001:0.231541:0.464001:0.216106:0.421830:0.216106:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.744491:0.231541:0.749184:0.231541:0.749184:0.216106:0.744491:0.216106:0.000000
A:@0.866126:0.231541:0.876010:0.231541:0.876010:0.216106:0.866126:0.216106:0.000000
B g:@0.902001:0.231541:0.926870:0.231541:0.926870:0.216106:0.902001:0.216106:0.000000:0.000000:0.000000
una función de   en  . La composición de la función   con la de  , que se nota :@0.293623:0.248183:0.861818:0.248183:0.861818:0.232470:0.293623:0.232470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.407638:0.248183:0.416473:0.248183:0.416473:0.232747:0.407638:0.232747:0.000000
C:@0.442943:0.248183:0.452846:0.248183:0.452846:0.232747:0.442943:0.232747:0.000000
g:@0.677138:0.248183:0.686397:0.248183:0.686397:0.232747:0.677138:0.232747:0.000000
f:@0.760652:0.248183:0.765346:0.248183:0.765346:0.232747:0.760652:0.232747:0.000000
g   f:@0.861671:0.248183:0.888104:0.248183:0.888104:0.232747:0.861671:0.232747:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.874114:0.248585:0.880244:0.248585:0.880244:0.235687:0.874114:0.235687:0.000000
, es la :@0.888030:0.248183:0.930938:0.248183:0.930938:0.232470:0.888030:0.232470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función de   en   definida como sigue:@0.293623:0.264825:0.574776:0.264825:0.574776:0.249112:0.293623:0.249112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.375922:0.264825:0.385807:0.264825:0.385807:0.249389:0.375922:0.249389:0.000000
C:@0.412258:0.264825:0.422161:0.264825:0.422161:0.249389:0.412258:0.249389:0.000000
(:@0.514179:0.288081:0.519057:0.288081:0.519057:0.272369:0.514179:0.272369:0.000000
g   f x:@0.518983:0.288081:0.562388:0.288081:0.562388:0.272646:0.518983:0.272646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.531427:0.288484:0.537556:0.288484:0.537556:0.275586:0.531427:0.275586:0.000000
)( )   ( ( ( )),   :@0.545343:0.288081:0.650522:0.288081:0.650522:0.272369:0.545343:0.272369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.571057:0.287527:0.586391:0.287527:0.586391:0.273811:0.571057:0.273811:0.000000
g f x:@0.595042:0.288081:0.625911:0.288081:0.625911:0.272646:0.595042:0.272646:0.000000:0.000000:0.000000:0.000000:0.000000
;:@0.650411:0.287527:0.662689:0.287527:0.662689:0.273811:0.650411:0.273811:0.000000
x:@0.662597:0.288081:0.670052:0.288081:0.670052:0.272646:0.662597:0.272646:0.000000
   :@0.669978:0.288081:0.693208:0.288081:0.693208:0.272369:0.669978:0.272369:0.000000:0.000000:0.000000
[:@0.673936:0.287943:0.689269:0.287943:0.689269:0.273894:0.673936:0.273894:0.000000
A.:@0.693134:0.288081:0.706277:0.288081:0.706277:0.272646:0.693134:0.272646:0.000000:0.000000
De la definición se tiene :@0.293605:0.315749:0.471209:0.315749:0.471209:0.300036:0.293605:0.300036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.470959:0.315749:0.497373:0.315749:0.497373:0.300313:0.470959:0.300313:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.483402:0.316151:0.489532:0.316151:0.489532:0.303253:0.483402:0.303253:0.000000
: :@0.497318:0.315749:0.504478:0.315749:0.504478:0.300036:0.497318:0.300036:0.000000:0.000000
A:@0.518799:0.308551:0.528684:0.308551:0.528684:0.293116:0.518799:0.293116:0.000000
    ,:@0.528610:0.308551:0.568186:0.308551:0.568186:0.292838:0.528610:0.292838:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.532568:0.308135:0.550736:0.308135:0.550736:0.291146:0.532568:0.291146:0.000000
C:@0.554601:0.308551:0.564504:0.308551:0.564504:0.293116:0.554601:0.293116:0.000000
x:@0.518799:0.325193:0.526254:0.325193:0.526254:0.309757:0.518799:0.309757:0.000000
   (:@0.526181:0.325193:0.557050:0.325193:0.557050:0.309480:0.526181:0.309480:0.000000:0.000000:0.000000:0.000000
→:@0.530138:0.324777:0.548306:0.324777:0.548306:0.307788:0.530138:0.307788:0.000000
g   f x:@0.556957:0.325193:0.600362:0.325193:0.600362:0.309757:0.556957:0.309757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.569401:0.325595:0.575530:0.325595:0.575530:0.312698:0.569401:0.312698:0.000000
)( )    ( ( )).:@0.583317:0.325193:0.671837:0.325193:0.671837:0.309480:0.583317:0.309480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.609032:0.324638:0.624365:0.324638:0.624365:0.310922:0.609032:0.310922:0.000000
g f x:@0.628230:0.325193:0.659099:0.325193:0.659099:0.309757:0.628230:0.309757:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.708575:0.315740:0.712606:0.315740:0.712606:0.300027:0.708575:0.300027:0.000000
Ejercicios resueltos:@0.293660:0.338993:0.436670:0.338993:0.436670:0.322323:0.293660:0.322323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Sean     { 30,  25,  20,  15},     {0, 1, 2, 3, 4},:@0.293660:0.362246:0.683889:0.362246:0.683889:0.346533:0.293660:0.346533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.363271:0.362246:0.373156:0.362246:0.373156:0.346811:0.363271:0.346811:0.000000
5 2:@0.377040:0.361691:0.416358:0.361691:0.416358:0.347976:0.377040:0.347976:0.000000:0.000000:0.000000
2:@0.441134:0.361691:0.456467:0.361691:0.456467:0.347976:0.441134:0.347976:0.000000
2:@0.481243:0.361691:0.496577:0.361691:0.496577:0.347976:0.481243:0.347976:0.000000
2:@0.521353:0.361691:0.536686:0.361691:0.536686:0.347976:0.521353:0.347976:0.000000
B:@0.566267:0.362246:0.575102:0.362246:0.575102:0.346811:0.566267:0.346811:0.000000
5:@0.578986:0.361691:0.594319:0.361691:0.594319:0.347976:0.578986:0.347976:0.000000
 :@0.293660:0.385499:0.297691:0.385499:0.297691:0.369787:0.293660:0.369787:0.000000
C:@0.323781:0.385499:0.333684:0.385499:0.333684:0.370064:0.323781:0.370064:0.000000
   {10, 20, 30, 40, 50},   y   son las funciones que se muestran en los siguientes :@0.333758:0.385499:0.931075:0.385499:0.931075:0.369787:0.333758:0.369787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.338691:0.384945:0.354024:0.384945:0.354024:0.371229:0.338691:0.371229:0.000000
f g:@0.500785:0.385499:0.532869:0.385499:0.532869:0.370064:0.500785:0.370064:0.000000:0.000000:0.000000
diagramas de Venn-Euler: :@0.323763:0.402141:0.511682:0.402141:0.511682:0.386428:0.323763:0.386428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.424874:0.432881:0.439510:0.432881:0.439510:0.419788:0.424874:0.419788:0.000000
30:@0.439511:0.433410:0.456660:0.433410:0.456660:0.418412:0.439511:0.418412:0.000000:0.000000
2:@0.424875:0.448766:0.439511:0.448766:0.439511:0.435674:0.424875:0.435674:0.000000
25:@0.439511:0.449295:0.456660:0.449295:0.456660:0.434297:0.439511:0.434297:0.000000:0.000000
2:@0.424875:0.464651:0.439511:0.464651:0.439511:0.451559:0.424875:0.451559:0.000000
20:@0.439511:0.465181:0.456660:0.465181:0.456660:0.450182:0.439511:0.450182:0.000000:0.000000
2:@0.424875:0.480537:0.439511:0.480537:0.439511:0.467445:0.424875:0.467445:0.000000
15:@0.439511:0.481066:0.456660:0.481066:0.456660:0.466068:0.439511:0.466068:0.000000:0.000000
0:@0.524464:0.429505:0.533039:0.429505:0.533039:0.414506:0.524464:0.414506:0.000000
1:@0.524464:0.443378:0.533039:0.443378:0.533039:0.428380:0.524464:0.428380:0.000000
2:@0.524464:0.457251:0.533039:0.457251:0.533039:0.442253:0.524464:0.442253:0.000000
3:@0.524464:0.471125:0.533039:0.471125:0.533039:0.456126:0.524464:0.456126:0.000000
4:@0.524464:0.484998:0.533039:0.484998:0.533039:0.469999:0.524464:0.469999:0.000000
0:@0.688152:0.429531:0.696726:0.429531:0.696726:0.414533:0.688152:0.414533:0.000000
1:@0.688152:0.443405:0.696726:0.443405:0.696726:0.428406:0.688152:0.428406:0.000000
2:@0.688152:0.457278:0.696726:0.457278:0.696726:0.442279:0.688152:0.442279:0.000000
3:@0.688152:0.471151:0.696726:0.471151:0.696726:0.456153:0.688152:0.456153:0.000000
4:@0.688152:0.485024:0.696726:0.485024:0.696726:0.470026:0.688152:0.470026:0.000000
10:@0.771858:0.424038:0.789007:0.424038:0.789007:0.409039:0.771858:0.409039:0.000000:0.000000
20:@0.771858:0.437024:0.789007:0.437024:0.789007:0.422026:0.771858:0.422026:0.000000:0.000000
30:@0.771858:0.450010:0.789007:0.450010:0.789007:0.435012:0.771858:0.435012:0.000000:0.000000
40:@0.771858:0.462997:0.789007:0.462997:0.789007:0.447998:0.771858:0.447998:0.000000:0.000000
50:@0.771858:0.475983:0.789007:0.475983:0.789007:0.460984:0.771858:0.460984:0.000000:0.000000
60:@0.771858:0.488969:0.789007:0.488969:0.789007:0.473971:0.771858:0.473971:0.000000:0.000000
A:@0.395725:0.421350:0.405160:0.421350:0.405160:0.406617:0.395725:0.406617:0.000000
B:@0.647898:0.421350:0.656332:0.421350:0.656332:0.406617:0.647898:0.406617:0.000000
B:@0.564209:0.421350:0.572643:0.421350:0.572643:0.406617:0.564209:0.406617:0.000000
C:@0.815380:0.435647:0.824833:0.435647:0.824833:0.420914:0.815380:0.420914:0.000000
f:@0.482506:0.421350:0.486986:0.421350:0.486986:0.406617:0.482506:0.406617:0.000000
f:@0.734187:0.421350:0.738667:0.421350:0.738667:0.406617:0.734187:0.406617:0.000000
 :@0.293660:0.516981:0.297691:0.516981:0.297691:0.501268:0.293660:0.501268:0.000000
La función :@0.323774:0.516981:0.403883:0.516981:0.403883:0.501268:0.323774:0.501268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.403737:0.516981:0.430152:0.516981:0.430152:0.501546:0.403737:0.501546:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.416180:0.517383:0.422310:0.517383:0.422310:0.504486:0.416180:0.504486:0.000000
 está definida del modo que se indica a continuación::@0.430096:0.516981:0.816888:0.516981:0.816888:0.501268:0.430096:0.501268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.293660:0.540234:0.297691:0.540234:0.297691:0.524522:0.293660:0.524522:0.000000
g   f:@0.323781:0.540234:0.350195:0.540234:0.350195:0.524799:0.323781:0.524799:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.336224:0.540636:0.342354:0.540636:0.342354:0.527739:0.336224:0.527739:0.000000
( 30)    ( ( 30))    (4)   20,:@0.350140:0.540234:0.576973:0.540234:0.576973:0.524522:0.350140:0.524522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.354945:0.539680:0.370278:0.539680:0.370278:0.525964:0.354945:0.525964:0.000000
5:@0.396729:0.539680:0.412062:0.539680:0.412062:0.525964:0.396729:0.525964:0.000000
g f:@0.415928:0.540234:0.434611:0.540234:0.434611:0.524799:0.415928:0.524799:0.000000:0.000000:0.000000
2:@0.439342:0.539680:0.454675:0.539680:0.454675:0.525964:0.439342:0.525964:0.000000
5:@0.485931:0.539680:0.501264:0.539680:0.501264:0.525964:0.485931:0.525964:0.000000
g:@0.505129:0.540234:0.514388:0.540234:0.514388:0.524799:0.505129:0.524799:0.000000
5:@0.536753:0.539680:0.552086:0.539680:0.552086:0.525964:0.536753:0.525964:0.000000
 :@0.293660:0.563487:0.297691:0.563487:0.297691:0.547775:0.293660:0.547775:0.000000
g   f:@0.323781:0.563487:0.350195:0.563487:0.350195:0.548052:0.323781:0.548052:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.336224:0.563890:0.342354:0.563890:0.342354:0.550992:0.336224:0.550992:0.000000
( 25)    ( ( 25))    (2)   60,:@0.350140:0.563487:0.576973:0.563487:0.576973:0.547775:0.350140:0.547775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.354945:0.562933:0.370278:0.562933:0.370278:0.549217:0.354945:0.549217:0.000000
5:@0.396729:0.562933:0.412062:0.562933:0.412062:0.549217:0.396729:0.549217:0.000000
g f:@0.415928:0.563487:0.434611:0.563487:0.434611:0.548052:0.415928:0.548052:0.000000:0.000000:0.000000
2:@0.439342:0.562933:0.454675:0.562933:0.454675:0.549217:0.439342:0.549217:0.000000
5:@0.485931:0.562933:0.501264:0.562933:0.501264:0.549217:0.485931:0.549217:0.000000
g:@0.505129:0.563487:0.514388:0.563487:0.514388:0.548052:0.505129:0.548052:0.000000
5:@0.536753:0.562933:0.552086:0.562933:0.552086:0.549217:0.536753:0.549217:0.000000
 :@0.293660:0.586741:0.297691:0.586741:0.297691:0.571028:0.293660:0.571028:0.000000
g   f:@0.323781:0.586741:0.350195:0.586741:0.350195:0.571305:0.323781:0.571305:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.336224:0.587143:0.342354:0.587143:0.342354:0.574245:0.336224:0.574245:0.000000
( 20)    ( ( 20))    (0)   40,:@0.350140:0.586741:0.576973:0.586741:0.576973:0.571028:0.350140:0.571028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.354945:0.586186:0.370278:0.586186:0.370278:0.572470:0.354945:0.572470:0.000000
5:@0.396729:0.586186:0.412062:0.586186:0.412062:0.572470:0.396729:0.572470:0.000000
g f:@0.415928:0.586741:0.434611:0.586741:0.434611:0.571305:0.415928:0.571305:0.000000:0.000000:0.000000
2:@0.439342:0.586186:0.454675:0.586186:0.454675:0.572470:0.439342:0.572470:0.000000
5:@0.485931:0.586186:0.501264:0.586186:0.501264:0.572470:0.485931:0.572470:0.000000
g:@0.505129:0.586741:0.514388:0.586741:0.514388:0.571305:0.505129:0.571305:0.000000
5:@0.536753:0.586186:0.552086:0.586186:0.552086:0.572470:0.536753:0.572470:0.000000
g   f:@0.323781:0.609998:0.350195:0.609998:0.350195:0.594562:0.323781:0.594562:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.336224:0.610400:0.342354:0.610400:0.342354:0.597502:0.336224:0.597502:0.000000
( 15)    ( ( 15))    (3)   30.:@0.350140:0.609998:0.576973:0.609998:0.576973:0.594285:0.350140:0.594285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.354945:0.609443:0.370278:0.609443:0.370278:0.595727:0.354945:0.595727:0.000000
5:@0.396729:0.609443:0.412062:0.609443:0.412062:0.595727:0.396729:0.595727:0.000000
g f:@0.415928:0.609998:0.434611:0.609998:0.434611:0.594562:0.415928:0.594562:0.000000:0.000000:0.000000
2:@0.439342:0.609443:0.454675:0.609443:0.454675:0.595727:0.439342:0.595727:0.000000
5:@0.485931:0.609443:0.501264:0.609443:0.501264:0.595727:0.485931:0.595727:0.000000
g:@0.505129:0.609998:0.514388:0.609998:0.514388:0.594562:0.505129:0.594562:0.000000
5:@0.536753:0.609443:0.552086:0.609443:0.552086:0.595727:0.536753:0.595727:0.000000
En la Figura 7.1 se muestran los resultados de la función :@0.323781:0.633255:0.730283:0.633255:0.730283:0.617542:0.323781:0.617542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.729827:0.633255:0.755505:0.633255:0.755505:0.617819:0.729827:0.617819:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.741902:0.633657:0.748031:0.633657:0.748031:0.620759:0.741902:0.620759:0.000000
.:@0.755266:0.633255:0.758468:0.633255:0.758468:0.617542:0.755266:0.617542:0.000000
Ejercicios resueltos:@0.323799:0.656512:0.466809:0.656512:0.466809:0.639842:0.323799:0.639842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  Sean     {1, 2, 3, 4},          . Consideremos las funciones  ,   definidas como :@0.323781:0.679755:0.930996:0.679755:0.930996:0.664042:0.323781:0.664042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.393466:0.679755:0.403351:0.679755:0.403351:0.664319:0.393466:0.664319:0.000000
5:@0.407308:0.679200:0.422641:0.679200:0.422641:0.665484:0.407308:0.665484:0.000000
B:@0.500394:0.679755:0.509229:0.679755:0.509229:0.664319:0.500394:0.664319:0.000000
5 5:@0.513187:0.679200:0.561653:0.679200:0.561653:0.665484:0.513187:0.665484:0.000000:0.000000:0.000000
C:@0.532459:0.679755:0.542362:0.679755:0.542362:0.664319:0.532459:0.664319:0.000000
A:@0.565592:0.679755:0.575477:0.679755:0.575477:0.664319:0.565592:0.664319:0.000000
f g:@0.789388:0.679755:0.810427:0.679755:0.810427:0.664319:0.789388:0.664319:0.000000:0.000000:0.000000
sigue::@0.353872:0.696396:0.396135:0.696396:0.396135:0.680684:0.353872:0.680684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.323781:0.719650:0.327812:0.719650:0.327812:0.703937:0.323781:0.703937:0.000000
f:@0.353902:0.719650:0.358596:0.719650:0.358596:0.704214:0.353902:0.704214:0.000000
(1)   2,     (2)   3,     (3)   4,     (4)   1,:@0.358522:0.719650:0.634484:0.719650:0.634484:0.703937:0.358522:0.703937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.380961:0.719095:0.396294:0.719095:0.396294:0.705379:0.380961:0.705379:0.000000
f:@0.427973:0.719650:0.432667:0.719650:0.432667:0.704214:0.427973:0.704214:0.000000
5:@0.455031:0.719095:0.470365:0.719095:0.470365:0.705379:0.455031:0.705379:0.000000
f:@0.502044:0.719650:0.506737:0.719650:0.506737:0.704214:0.502044:0.704214:0.000000
5:@0.529102:0.719095:0.544436:0.719095:0.544436:0.705379:0.529102:0.705379:0.000000
f:@0.576114:0.719650:0.580808:0.719650:0.580808:0.704214:0.576114:0.704214:0.000000
5:@0.603173:0.719095:0.618506:0.719095:0.618506:0.705379:0.603173:0.705379:0.000000
 :@0.323781:0.742903:0.327812:0.742903:0.327812:0.727190:0.323781:0.727190:0.000000
g:@0.353902:0.742903:0.363161:0.742903:0.363161:0.727468:0.353902:0.727468:0.000000
(1)   3,     (2)   4,     (3)   1,     (4)   2.:@0.363087:0.742903:0.652744:0.742903:0.652744:0.727190:0.363087:0.727190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.385526:0.742348:0.400859:0.742348:0.400859:0.728632:0.385526:0.728632:0.000000
g:@0.432538:0.742903:0.441797:0.742903:0.441797:0.727468:0.432538:0.727468:0.000000
5:@0.464161:0.742348:0.479495:0.742348:0.479495:0.728632:0.464161:0.728632:0.000000
g:@0.511174:0.742903:0.520432:0.742903:0.520432:0.727468:0.511174:0.727468:0.000000
5:@0.542797:0.742348:0.558131:0.742348:0.558131:0.728632:0.542797:0.728632:0.000000
g:@0.589809:0.742903:0.599068:0.742903:0.599068:0.727468:0.589809:0.727468:0.000000
5:@0.621433:0.742348:0.636766:0.742348:0.636766:0.728632:0.621433:0.728632:0.000000
 :@0.323781:0.766156:0.327812:0.766156:0.327812:0.750443:0.323781:0.750443:0.000000
Claramente,  las  funciones  ,    son  inyectivas,  sobreyectivas  y  biyectivas. :@0.353895:0.766156:0.930820:0.766156:0.930820:0.750443:0.353895:0.750443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.564545:0.766156:0.589634:0.766156:0.589634:0.750721:0.564545:0.750721:0.000000:0.000000:0.000000
Determinemos la función :@0.353910:0.782798:0.543189:0.782798:0.543189:0.767085:0.353910:0.767085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.542971:0.782798:0.568649:0.782798:0.568649:0.767363:0.542971:0.767363:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.555046:0.783200:0.561176:0.783200:0.561176:0.770303:0.555046:0.770303:0.000000
. Tenemos: :@0.568410:0.782798:0.648237:0.782798:0.648237:0.767085:0.568410:0.767085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.353895:0.806051:0.358773:0.806051:0.358773:0.790338:0.353895:0.790338:0.000000
g   f:@0.358700:0.806051:0.385114:0.806051:0.385114:0.790616:0.358700:0.790616:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.371143:0.806453:0.377273:0.806453:0.377273:0.793556:0.371143:0.793556:0.000000
)(1)    ( (1))    (2)   4,   (:@0.385059:0.806051:0.576163:0.806051:0.576163:0.790338:0.385059:0.790338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.412302:0.805496:0.427635:0.805496:0.427635:0.791781:0.412302:0.791781:0.000000
g f:@0.431500:0.806051:0.450184:0.806051:0.450184:0.790616:0.431500:0.790616:0.000000:0.000000:0.000000
5:@0.477353:0.805496:0.492686:0.805496:0.492686:0.791781:0.477353:0.791781:0.000000
g:@0.496552:0.806051:0.505810:0.806051:0.505810:0.790616:0.496552:0.790616:0.000000
5:@0.528175:0.805496:0.543508:0.805496:0.543508:0.791781:0.528175:0.791781:0.000000
g   f:@0.576034:0.806051:0.602448:0.806051:0.602448:0.790616:0.576034:0.790616:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.588477:0.806453:0.594607:0.806453:0.594607:0.793556:0.588477:0.793556:0.000000
)(2)    ( (2))    (3)   1,:@0.602393:0.806051:0.776820:0.806051:0.776820:0.790338:0.602393:0.790338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.629636:0.805496:0.644969:0.805496:0.644969:0.791781:0.629636:0.791781:0.000000
g f:@0.648835:0.806051:0.667518:0.806051:0.667518:0.790616:0.648835:0.790616:0.000000:0.000000:0.000000
5:@0.694687:0.805496:0.710020:0.805496:0.710020:0.791781:0.694687:0.791781:0.000000
g:@0.713886:0.806051:0.723145:0.806051:0.723145:0.790616:0.713886:0.790616:0.000000
5:@0.745510:0.805496:0.760843:0.805496:0.760843:0.791781:0.745510:0.791781:0.000000
(:@0.353895:0.829304:0.358773:0.829304:0.358773:0.813592:0.353895:0.813592:0.000000
g   f:@0.358700:0.829304:0.385114:0.829304:0.385114:0.813869:0.358700:0.813869:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.371143:0.829706:0.377273:0.829706:0.377273:0.816809:0.371143:0.816809:0.000000
)(3)    ( (3))    (4)   2,   (:@0.385059:0.829304:0.576163:0.829304:0.576163:0.813592:0.385059:0.813592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.412302:0.828749:0.427635:0.828749:0.427635:0.815034:0.412302:0.815034:0.000000
g f:@0.431500:0.829304:0.450184:0.829304:0.450184:0.813869:0.431500:0.813869:0.000000:0.000000:0.000000
5:@0.477353:0.828749:0.492686:0.828749:0.492686:0.815034:0.477353:0.815034:0.000000
g:@0.496552:0.829304:0.505810:0.829304:0.505810:0.813869:0.496552:0.813869:0.000000
5:@0.528175:0.828749:0.543508:0.828749:0.543508:0.815034:0.528175:0.815034:0.000000
g   f:@0.576034:0.829304:0.602448:0.829304:0.602448:0.813869:0.576034:0.813869:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.588477:0.829706:0.594607:0.829706:0.594607:0.816809:0.588477:0.816809:0.000000
)(4)    ( (4))    (1)   3.:@0.602393:0.829304:0.776820:0.829304:0.776820:0.813592:0.602393:0.813592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.629636:0.828749:0.644969:0.828749:0.644969:0.815034:0.629636:0.815034:0.000000
g f:@0.648835:0.829304:0.667518:0.829304:0.667518:0.813869:0.648835:0.813869:0.000000:0.000000:0.000000
5:@0.694687:0.828749:0.710020:0.828749:0.710020:0.815034:0.694687:0.815034:0.000000
g:@0.713886:0.829304:0.723145:0.829304:0.723145:0.813869:0.713886:0.813869:0.000000
5:@0.745510:0.828749:0.760843:0.828749:0.760843:0.815034:0.745510:0.815034:0.000000
 :@0.323781:0.852557:0.327812:0.852557:0.327812:0.836845:0.323781:0.836845:0.000000
Observamos que :@0.353895:0.852557:0.482932:0.852557:0.482932:0.836845:0.353895:0.836845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.483203:0.852557:0.509599:0.852557:0.509599:0.837122:0.483203:0.837122:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.495628:0.852960:0.501757:0.852960:0.501757:0.840062:0.495628:0.840062:0.000000
 es inyectiva, sobreyectiva, biyectiva. ¿Cómo está definida :@0.509360:0.852557:0.931212:0.852557:0.931212:0.836845:0.509360:0.836845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función compuesta :@0.353892:0.869199:0.515802:0.869199:0.515802:0.853487:0.353892:0.853487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f   g:@0.515581:0.869199:0.541259:0.869199:0.541259:0.853764:0.515581:0.853764:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.523091:0.869601:0.529221:0.869601:0.529221:0.856704:0.523091:0.856704:0.000000
?, ¿es :@0.541020:0.869199:0.581663:0.869199:0.581663:0.853487:0.541020:0.853487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f   g:@0.581535:0.869199:0.607213:0.869199:0.607213:0.853764:0.581535:0.853764:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.589045:0.869601:0.595174:0.869601:0.595174:0.856704:0.589045:0.856704:0.000000
   :@0.606973:0.869199:0.630203:0.869199:0.630203:0.853487:0.606973:0.853487:0.000000:0.000000:0.000000
5:@0.610931:0.868644:0.626264:0.868644:0.626264:0.854929:0.610931:0.854929:0.000000
g   f:@0.630130:0.869199:0.655808:0.869199:0.655808:0.853764:0.630130:0.853764:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.642205:0.869601:0.648334:0.869601:0.648334:0.856704:0.642205:0.856704:0.000000
?:@0.655568:0.869199:0.662582:0.869199:0.662582:0.853487:0.655568:0.853487:0.000000
3.  Sean  ,   las funciones definidas de   en   que se especifican:@0.323781:0.892452:0.805770:0.892452:0.805770:0.876740:0.323781:0.876740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.393392:0.892452:0.417248:0.892452:0.417248:0.877017:0.393392:0.877017:0.000000:0.000000:0.000000
Q:@0.611481:0.891593:0.626815:0.891593:0.626815:0.878695:0.611481:0.878695:0.000000
Q:@0.653247:0.891593:0.668581:0.891593:0.668581:0.878695:0.653247:0.878695:0.000000
 :@0.323781:0.917022:0.327812:0.917022:0.327812:0.901309:0.323781:0.901309:0.000000
a continuación:  ( )       1,     ( )         1,   :@0.353895:0.917022:0.710275:0.917022:0.710275:0.901309:0.353895:0.901309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u x:@0.469349:0.917022:0.490849:0.917022:0.490849:0.901587:0.469349:0.901587:0.000000:0.000000:0.000000
5:@0.499518:0.916467:0.514852:0.916467:0.514852:0.902752:0.499518:0.902752:0.000000
x:@0.518717:0.917022:0.526172:0.917022:0.526172:0.901587:0.518717:0.901587:0.000000
2:@0.526110:0.910958:0.531347:0.910958:0.531347:0.901798:0.526110:0.901798:0.000000
1:@0.535259:0.916467:0.550592:0.916467:0.550592:0.902752:0.535259:0.902752:0.000000
v x:@0.582271:0.917022:0.602187:0.917022:0.602187:0.901587:0.582271:0.901587:0.000000:0.000000:0.000000
5 2:@0.610857:0.916467:0.645389:0.916467:0.645389:0.902752:0.610857:0.902752:0.000000:0.000000:0.000000
x:@0.652722:0.909718:0.658822:0.909718:0.658822:0.897089:0.652722:0.897089:0.000000
3:@0.652090:0.923583:0.659439:0.923583:0.659439:0.910728:0.652090:0.910728:0.000000
 :@0.659439:0.923583:0.662737:0.923583:0.662737:0.910728:0.659439:0.910728:0.000000
2:@0.667091:0.916467:0.682425:0.916467:0.682425:0.902752:0.667091:0.902752:0.000000
;:@0.710164:0.916467:0.722442:0.916467:0.722442:0.902752:0.710164:0.902752:0.000000
x:@0.722350:0.917022:0.729805:0.917022:0.729805:0.901587:0.722350:0.901587:0.000000
    .:@0.729731:0.917022:0.771332:0.917022:0.771332:0.901309:0.729731:0.901309:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.733689:0.916883:0.749022:0.916883:0.749022:0.902835:0.733689:0.902835:0.000000
Q:@0.752888:0.916162:0.768221:0.916162:0.768221:0.903265:0.752888:0.903265:0.000000
 :@0.293660:0.940275:0.297691:0.940275:0.297691:0.924563:0.293660:0.924563:0.000000
Determinemos las funciones compuestas      y  :@0.353907:0.940275:0.711761:0.940275:0.711761:0.924563:0.353907:0.924563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v  u:@0.658233:0.940275:0.688089:0.940275:0.688089:0.924840:0.658233:0.924840:0.000000:0.000000:0.000000:0.000000
+:@0.668780:0.940678:0.674909:0.940678:0.674909:0.927780:0.668780:0.927780:0.000000
u   v:@0.711650:0.940275:0.740605:0.940275:0.740605:0.924840:0.711650:0.924840:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.723781:0.940678:0.729910:0.940678:0.729910:0.927780:0.723781:0.927780:0.000000
.:@0.740366:0.940275:0.743569:0.940275:0.743569:0.924563:0.740366:0.924563:0.000000
Tema 7. Composición de funciones y funciones inversas:@0.073089:0.098522:0.890561:0.098522:0.890561:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo representas en un diagrama de Venn la composición de funciones?:@0.307891:0.164439:0.829684:0.164439:0.829684:0.149441:0.307891:0.149441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema:@0.082576:0.311628:0.142577:0.311628:0.142577:0.296474:0.082576:0.296474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.142488:0.311628:0.146437:0.311628:0.146437:0.296222:0.142488:0.296222:0.000000
 Sean  ,  ,   :@0.146370:0.311628:0.228199:0.311628:0.228199:0.297344:0.146370:0.297344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.185795:0.311628:0.224534:0.311628:0.224534:0.297596:0.185795:0.297596:0.000000:0.000000:0.000000:0.000000:0.000000
tres conjuntos no vacíos, :@0.082564:0.326757:0.248728:0.326757:0.248728:0.312473:0.082564:0.312473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.082564:0.341886:0.086831:0.341886:0.086831:0.327854:0.082564:0.327854:0.000000
 una función de   en  , :@0.086764:0.341886:0.241569:0.341886:0.241569:0.327602:0.086764:0.327602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.193995:0.341886:0.202981:0.341886:0.202981:0.327854:0.193995:0.327854:0.000000
B:@0.227028:0.341886:0.235060:0.341886:0.235060:0.327854:0.227028:0.327854:0.000000
g:@0.082547:0.357015:0.090964:0.357015:0.090964:0.342983:0.082547:0.342983:0.000000
 una función de   en  . :@0.090898:0.357015:0.245719:0.357015:0.245719:0.342731:0.090898:0.342731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.198128:0.357015:0.206160:0.357015:0.206160:0.342983:0.198128:0.342983:0.000000
C:@0.230207:0.357015:0.239210:0.357015:0.239210:0.342983:0.230207:0.342983:0.000000
Entonces,:@0.082531:0.372144:0.146240:0.372144:0.146240:0.357860:0.082531:0.357860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Si  ,   son inyectivas, :@0.082576:0.386359:0.232517:0.386359:0.232517:0.372789:0.082576:0.372789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.116022:0.386359:0.134542:0.386359:0.134542:0.373029:0.116022:0.373029:0.000000:0.000000:0.000000
g   f:@0.232866:0.386359:0.255726:0.386359:0.255726:0.373029:0.232866:0.373029:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.243629:0.386874:0.248922:0.386874:0.248922:0.375735:0.243629:0.375735:0.000000
es inyectiva.:@0.101556:0.400732:0.176843:0.400732:0.176843:0.387162:0.101556:0.387162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  Si  ,   son sobreyectivas, :@0.082576:0.420465:0.259176:0.420465:0.259176:0.406895:0.082576:0.406895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.116483:0.420465:0.135448:0.420465:0.135448:0.407134:0.116483:0.407134:0.000000:0.000000:0.000000
g   f:@0.101540:0.434837:0.123716:0.434837:0.123716:0.421507:0.101540:0.421507:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.111968:0.435352:0.117262:0.435352:0.117262:0.424214:0.111968:0.424214:0.000000
 es sobreyectiva.:@0.123509:0.434837:0.225784:0.434837:0.225784:0.421267:0.123509:0.421267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.  Si  ,   son biyectivas, :@0.082576:0.454570:0.232578:0.454570:0.232578:0.441000:0.082576:0.441000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.115974:0.454570:0.134463:0.454570:0.134463:0.441240:0.115974:0.441240:0.000000:0.000000:0.000000
g   f:@0.232930:0.454570:0.255726:0.454570:0.255726:0.441240:0.232930:0.441240:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.243660:0.455085:0.248954:0.455085:0.248954:0.443947:0.243660:0.443947:0.000000
es biyectiva.:@0.101555:0.468943:0.177263:0.468943:0.177263:0.455373:0.101555:0.455373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.  Si :@0.082576:0.488676:0.117476:0.488676:0.117476:0.475106:0.082576:0.475106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.122826:0.488676:0.155701:0.488676:0.155701:0.475346:0.122826:0.475346:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.138453:0.489191:0.143747:0.489191:0.143747:0.478052:0.138453:0.478052:0.000000
 es inyectiva, :@0.156226:0.488676:0.259176:0.488676:0.259176:0.475106:0.156226:0.475106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.101540:0.503049:0.105593:0.503049:0.105593:0.489718:0.101540:0.489718:0.000000
 es inyectiva.:@0.105371:0.503049:0.184075:0.503049:0.184075:0.489479:0.105371:0.489479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5.  Si :@0.082576:0.522782:0.116340:0.522782:0.116340:0.509212:0.082576:0.509212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.118327:0.522782:0.144565:0.522782:0.144565:0.509451:0.118327:0.509451:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.130727:0.523297:0.136021:0.523297:0.136021:0.512158:0.130727:0.512158:0.000000
 es sobreyectiva, :@0.144637:0.522782:0.259208:0.522782:0.259208:0.509212:0.144637:0.509212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.101571:0.537154:0.109568:0.537154:0.109568:0.523824:0.101571:0.523824:0.000000
 es sobreyectiva.:@0.109345:0.537154:0.211619:0.537154:0.211619:0.523584:0.109345:0.523584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.268346:0.187141:0.268346:0.187141:0.251399:0.078581:0.251399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.284988:0.176057:0.284988:0.176057:0.268041:0.078581:0.268041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.127067:0.664853:0.141703:0.664853:0.141703:0.651760:0.127067:0.651760:0.000000
30:@0.141703:0.665382:0.158852:0.665382:0.158852:0.650384:0.141703:0.650384:0.000000:0.000000
2:@0.127067:0.680738:0.141703:0.680738:0.141703:0.667646:0.127067:0.667646:0.000000
25:@0.141703:0.681268:0.158852:0.681268:0.158852:0.666269:0.141703:0.666269:0.000000:0.000000
2:@0.127067:0.696623:0.141703:0.696623:0.141703:0.683531:0.127067:0.683531:0.000000
20:@0.141703:0.697153:0.158852:0.697153:0.158852:0.682154:0.141703:0.682154:0.000000:0.000000
2:@0.127067:0.712509:0.141703:0.712509:0.141703:0.699417:0.127067:0.699417:0.000000
15:@0.141703:0.713038:0.158852:0.713038:0.158852:0.698040:0.141703:0.698040:0.000000:0.000000
10:@0.222370:0.656950:0.239519:0.656950:0.239519:0.641951:0.222370:0.641951:0.000000:0.000000
20:@0.222370:0.669936:0.239519:0.669936:0.239519:0.654937:0.222370:0.654937:0.000000:0.000000
30:@0.222370:0.682922:0.239519:0.682922:0.239519:0.667924:0.222370:0.667924:0.000000:0.000000
40:@0.222370:0.695909:0.239519:0.695909:0.239519:0.680910:0.222370:0.680910:0.000000:0.000000
50:@0.222370:0.708895:0.239519:0.708895:0.239519:0.693896:0.222370:0.693896:0.000000:0.000000
60:@0.222370:0.721881:0.239519:0.721881:0.239519:0.706883:0.222370:0.706883:0.000000:0.000000
A:@0.097917:0.653283:0.107353:0.653283:0.107353:0.638549:0.097917:0.638549:0.000000
C:@0.265910:0.665793:0.275362:0.665793:0.275362:0.651059:0.265910:0.651059:0.000000
g   f:@0.174701:0.649497:0.200691:0.649475:0.200691:0.634742:0.174701:0.634763:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.186358:0.650034:0.192487:0.650034:0.192487:0.637136:0.186358:0.637136:0.000000
Figura 7.1:@0.249078:0.746568:0.300402:0.746568:0.300402:0.735140:0.249078:0.735140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t.ly/xW96B:@0.104396:0.932345:0.180421:0.932345:0.180421:0.916633:0.104396:0.916633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Funciones :@0.080269:0.800890:0.164352:0.800890:0.164352:0.783943:0.080269:0.783943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inversas:@0.080269:0.817531:0.144560:0.817531:0.144560:0.800584:0.080269:0.800584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000