54:@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 1. Sean :@0.293660:0.147965:0.363374:0.147965:0.363374:0.132252:0.293660:0.132252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A [ , 2]:@0.363235:0.147965:0.427844:0.147965:0.427844:0.132530:0.363235:0.132530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.376267:0.147410:0.391600:0.147410:0.391600:0.133694:0.376267:0.133694:0.000000 0:@0.399902:0.147965:0.408885:0.147965:0.408885:0.132252:0.399902:0.132252:0.000000 y :@0.427954:0.147965:0.451742:0.147965:0.451742:0.132252:0.427954:0.132252:0.000000:0.000000:0.000000:0.000000:0.000000 f, g F A:@0.451626:0.147965:0.514855:0.147965:0.514855:0.132530:0.451626:0.132530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.474551:0.147826:0.489884:0.147826:0.489884:0.133778:0.474551:0.133778:0.000000 S D:@0.500976:0.148547:0.518868:0.148547:0.518868:0.130893:0.500976:0.130893:0.000000:0.000000:0.000000 las funciones reales definidas como :@0.518776:0.147965:0.782808:0.147965:0.782808:0.132252:0.518776:0.132252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x x, g x x:@0.782478:0.147965:0.919343:0.147965:0.919343:0.132530:0.782478:0.132530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S D:@0.787098:0.148547:0.802560:0.148547:0.802560:0.130893:0.787098:0.130893:0.000000:0.000000:0.000000 5:@0.805690:0.147410:0.821023:0.147410:0.821023:0.133694:0.805690:0.133694:0.000000 2:@0.824152:0.147965:0.831846:0.147965:0.831846:0.132252:0.824152:0.132252:0.000000 S D:@0.854837:0.148547:0.870299:0.148547:0.870299:0.130893:0.854837:0.130893:0.000000:0.000000:0.000000 5:@0.873428:0.147410:0.888762:0.147410:0.888762:0.133694:0.873428:0.133694:0.000000 1:@0.894028:0.139988:0.903419:0.139988:0.903419:0.123561:0.894028:0.123561:0.000000 4:@0.894028:0.157430:0.903419:0.157430:0.903419:0.141003:0.894028:0.141003:0.000000 2 :@0.919269:0.141901:0.929262:0.141901:0.929262:0.132740:0.919269:0.132740:0.000000:0.000000:0.000000 ,:@0.923709:0.147965:0.926911:0.147965:0.926911:0.132252:0.923709:0.132252:0.000000 x :@0.323781:0.164607:0.352975:0.164607:0.352975:0.149171:0.323781:0.149171:0.000000:0.000000:0.000000:0.000000 [:@0.334420:0.164468:0.349754:0.164468:0.349754:0.150419:0.334420:0.150419:0.000000 [0, 2] La función está definida como:@0.353085:0.164607:0.630980:0.164607:0.630980:0.148894:0.353085:0.148894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.386826:0.164607:0.390158:0.164607:0.390158:0.149171:0.386826:0.149171:0.000000 fg:@0.473984:0.164607:0.487863:0.164607:0.487863:0.149171:0.473984:0.149171:0.000000:0.000000 S DS D:@0.323763:0.196060:0.361037:0.196060:0.361037:0.178406:0.323763:0.178406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg x f x g x x :@0.327757:0.195477:0.473763:0.195477:0.473763:0.180042:0.327757:0.180042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.364185:0.194923:0.379518:0.194923:0.379518:0.181207:0.364185:0.181207:0.000000 S D S D:@0.390544:0.196060:0.433820:0.196060:0.433820:0.178406:0.390544:0.178406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.436967:0.194923:0.452301:0.194923:0.452301:0.181207:0.436967:0.181207:0.000000 2:@0.455448:0.195477:0.463142:0.195477:0.463142:0.179765:0.455448:0.179765:0.000000 1:@0.480504:0.184977:0.489895:0.184977:0.489895:0.168550:0.480504:0.168550:0.000000 4:@0.480504:0.204940:0.489895:0.204940:0.489895:0.188514:0.480504:0.188514:0.000000 x x , x :@0.495143:0.195475:0.604741:0.195475:0.604741:0.180039:0.495143:0.180039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.502531:0.189411:0.507016:0.189411:0.507016:0.180250:0.502531:0.180250:0.000000 5:@0.514828:0.194920:0.530162:0.194920:0.530162:0.181204:0.514828:0.181204:0.000000 1:@0.535451:0.184977:0.544842:0.184977:0.544842:0.168550:0.535451:0.168550:0.000000 2:@0.535451:0.204941:0.544842:0.204941:0.544842:0.188514:0.535451:0.188514:0.000000 3:@0.560729:0.195475:0.565865:0.195475:0.565865:0.179762:0.560729:0.179762:0.000000 [:@0.586187:0.195336:0.601520:0.195336:0.601520:0.181288:0.586187:0.181288:0.000000 [0, 2]:@0.604851:0.195475:0.638482:0.195475:0.638482:0.179762:0.604851:0.179762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.638592:0.195475:0.641924:0.195475:0.641924:0.180039:0.638592:0.180039:0.000000 Calculemos algunas imágenes :@0.323791:0.222837:0.548131:0.222837:0.548131:0.207124:0.323791:0.207124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S DS D:@0.547863:0.223419:0.585137:0.223419:0.585137:0.205765:0.547863:0.205765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg x x :@0.551857:0.222837:0.620737:0.222837:0.620737:0.207401:0.551857:0.207401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.602182:0.222698:0.617516:0.222698:0.617516:0.208650:0.602182:0.208650:0.000000 [0, 2] Tenemos::@0.620663:0.222837:0.730216:0.222837:0.730216:0.207124:0.620663:0.207124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.654220:0.222837:0.660791:0.222837:0.660791:0.207401:0.654220:0.207401:0.000000:0.000000 x:@0.402499:0.265246:0.411187:0.265246:0.411187:0.249547:0.402499:0.249547:0.000000 f(x) x:@0.451683:0.265246:0.517176:0.265246:0.517176:0.249547:0.451683:0.249547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.480159:0.264691:0.495492:0.264691:0.495492:0.250975:0.480159:0.250975:0.000000 2:@0.498695:0.265246:0.508561:0.265246:0.508561:0.248299:0.498695:0.248299:0.000000 g(x) x:@0.563121:0.262514:0.636117:0.262512:0.636117:0.246814:0.563121:0.246815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.595922:0.261959:0.611256:0.261959:0.611256:0.248243:0.595922:0.248243:0.000000 1:@0.616938:0.253629:0.625011:0.253629:0.625011:0.239763:0.616938:0.239763:0.000000 4:@0.616938:0.267495:0.625011:0.267495:0.625011:0.253629:0.616938:0.253629:0.000000 :@0.625011:0.267495:0.628309:0.267495:0.628309:0.254639:0.625011:0.254639:0.000000 2:@0.636050:0.256449:0.641802:0.256449:0.641802:0.246568:0.636050:0.246568:0.000000 f(x)g(x) x:@0.702544:0.262512:0.803954:0.262512:0.803954:0.246814:0.702544:0.246814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.760508:0.261958:0.775841:0.261958:0.775841:0.248242:0.760508:0.248242:0.000000 1:@0.781536:0.253629:0.789608:0.253629:0.789608:0.239763:0.781536:0.239763:0.000000 2:@0.781536:0.267495:0.789608:0.267495:0.789608:0.253629:0.781536:0.253629:0.000000 :@0.789608:0.267495:0.792907:0.267495:0.792907:0.254639:0.789608:0.254639:0.000000 :@0.792026:0.262512:0.795340:0.262512:0.795340:0.247077:0.792026:0.247077:0.000000 3:@0.803894:0.256449:0.809646:0.256449:0.809646:0.246568:0.803894:0.246568:0.000000 0:@0.402352:0.297222:0.411334:0.297222:0.411334:0.281509:0.402352:0.281509:0.000000 0:@0.479938:0.297222:0.488921:0.297222:0.488921:0.281509:0.479938:0.281509:0.000000 0:@0.597965:0.297222:0.606948:0.297222:0.606948:0.281509:0.597965:0.281509:0.000000 0:@0.751611:0.297222:0.760594:0.297222:0.760594:0.281509:0.751611:0.281509:0.000000 1/2:@0.394713:0.325624:0.418992:0.325624:0.418992:0.309911:0.394713:0.309911:0.000000:0.000000:0.000000 1:@0.479938:0.325624:0.488921:0.325624:0.488921:0.309911:0.479938:0.309911:0.000000 1/16:@0.585872:0.325624:0.619060:0.325624:0.619060:0.309911:0.585872:0.309911:0.000000:0.000000:0.000000:0.000000 1/16:@0.739517:0.325624:0.772706:0.325624:0.772706:0.309911:0.739517:0.309911:0.000000:0.000000:0.000000:0.000000 1:@0.402352:0.354220:0.411334:0.354220:0.411334:0.338508:0.402352:0.338508:0.000000 2:@0.479938:0.354220:0.488921:0.354220:0.488921:0.338508:0.479938:0.338508:0.000000 1/4:@0.590326:0.354220:0.614606:0.354220:0.614606:0.338508:0.590326:0.338508:0.000000:0.000000:0.000000 1/2:@0.743972:0.354220:0.768251:0.354220:0.768251:0.338508:0.743972:0.338508:0.000000:0.000000:0.000000 2:@0.402352:0.382816:0.411334:0.382816:0.411334:0.367104:0.402352:0.367104:0.000000 4:@0.479938:0.382816:0.488921:0.382816:0.488921:0.367104:0.479938:0.367104:0.000000 1:@0.597965:0.382816:0.606948:0.382816:0.606948:0.367104:0.597965:0.367104:0.000000 4:@0.751611:0.382816:0.760594:0.382816:0.760594:0.367104:0.751611:0.367104:0.000000 En la Figura 6.3 se muestran las funciones :@0.323789:0.414547:0.631008:0.414547:0.631008:0.398834:0.323789:0.398834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g:@0.630638:0.414547:0.650434:0.414547:0.650434:0.399112:0.630638:0.399112:0.000000:0.000000:0.000000:0.000000 y :@0.650389:0.414547:0.699169:0.414547:0.699169:0.398834:0.650389:0.398834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg.:@0.674208:0.414547:0.691095:0.414547:0.691095:0.399112:0.674208:0.399112:0.000000:0.000000:0.000000 2. Considera las funciones reales :@0.293660:0.441900:0.544551:0.441900:0.544551:0.426187:0.293660:0.426187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g:@0.544270:0.441900:0.564065:0.441900:0.564065:0.426465:0.544270:0.426465:0.000000:0.000000:0.000000:0.000000 definidas en todo como siguen::@0.564021:0.441900:0.816937:0.441900:0.816937:0.426187:0.564021:0.426187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.699148:0.441761:0.714482:0.441761:0.714482:0.427713:0.699148:0.427713:0.000000 :@0.293660:0.495464:0.296973:0.495464:0.296973:0.480029:0.293660:0.480029:0.000000 f x:@0.353902:0.496335:0.369978:0.496335:0.369978:0.480900:0.353902:0.480900:0.000000:0.000000:0.000000 S D:@0.358529:0.496918:0.373991:0.496918:0.373991:0.479263:0.358529:0.479263:0.000000:0.000000:0.000000 :@0.373899:0.496335:0.377930:0.496335:0.377930:0.480622:0.373899:0.480622:0.000000 5:@0.377857:0.495780:0.393190:0.495780:0.393190:0.482065:0.377857:0.482065:0.000000 2:@0.405688:0.481815:0.421022:0.481815:0.421022:0.468099:0.405688:0.468099:0.000000 x, x ,:@0.420930:0.482370:0.496491:0.482370:0.496491:0.466935:0.420930:0.466935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si:@0.438085:0.482370:0.448725:0.482370:0.448725:0.466657:0.438085:0.466657:0.000000:0.000000 ,:@0.465770:0.481815:0.481103:0.481815:0.481103:0.468099:0.465770:0.468099:0.000000 0:@0.484251:0.482370:0.493233:0.482370:0.493233:0.466657:0.484251:0.466657:0.000000 2 si:@0.405707:0.503436:0.433723:0.503436:0.433723:0.487723:0.405707:0.487723:0.000000:0.000000:0.000000:0.000000 , x ,:@0.413327:0.503436:0.484729:0.503436:0.484729:0.488000:0.413327:0.488000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 $:@0.454007:0.502881:0.469341:0.502881:0.469341:0.489165:0.454007:0.489165:0.000000 0:@0.472488:0.503436:0.481471:0.503436:0.481471:0.487723:0.472488:0.487723:0.000000 :@0.531122:0.495464:0.537933:0.495464:0.537933:0.480029:0.531122:0.480029:0.000000:0.000000 g x :@0.594870:0.492919:0.622745:0.492919:0.622745:0.477483:0.594870:0.477483:0.000000:0.000000:0.000000:0.000000:0.000000 S D:@0.604062:0.493501:0.619524:0.493501:0.619524:0.475847:0.604062:0.475847:0.000000:0.000000:0.000000 5:@0.622671:0.492364:0.638005:0.492364:0.638005:0.478648:0.622671:0.478648:0.000000 1:@0.651792:0.466158:0.657430:0.466158:0.657430:0.449731:0.651792:0.449731:0.000000 x:@0.651792:0.482541:0.659585:0.482541:0.659585:0.466404:0.651792:0.466404:0.000000 , si x ,:@0.666427:0.475205:0.737149:0.475205:0.737149:0.459068:0.666427:0.459068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.705030:0.474625:0.721061:0.474625:0.721061:0.460286:0.705030:0.460286:0.000000 0:@0.724351:0.475205:0.733742:0.475205:0.733742:0.458778:0.724351:0.458778:0.000000 2:@0.649656:0.507344:0.664990:0.507344:0.664990:0.493628:0.649656:0.493628:0.000000 :@0.664898:0.507899:0.668211:0.507899:0.668211:0.492463:0.664898:0.492463:0.000000 1:@0.670279:0.499700:0.675918:0.499700:0.675918:0.483273:0.670279:0.483273:0.000000 2:@0.670279:0.519665:0.678323:0.519665:0.678323:0.503238:0.670279:0.503238:0.000000 x , si x .:@0.684915:0.508056:0.795029:0.508056:0.795029:0.491919:0.684915:0.491919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.699425:0.507476:0.715455:0.507476:0.715455:0.493137:0.699425:0.493137:0.000000 1:@0.718746:0.508056:0.724384:0.508056:0.724384:0.491629:0.718746:0.491629:0.000000 $:@0.762910:0.507476:0.778941:0.507476:0.778941:0.493137:0.762910:0.493137:0.000000 0:@0.782231:0.508056:0.791622:0.508056:0.791622:0.491629:0.782231:0.491629:0.000000 Definamos la función . Si :@0.323781:0.557691:0.523334:0.557691:0.523334:0.541978:0.323781:0.541978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg:@0.482194:0.557691:0.496073:0.557691:0.496073:0.542255:0.482194:0.542255:0.000000:0.000000 x , f x x, g x , :@0.523224:0.557691:0.711527:0.557691:0.711527:0.542255:0.523224:0.542255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.533863:0.557136:0.549196:0.557136:0.549196:0.543420:0.533863:0.543420:0.000000 0:@0.552344:0.557691:0.561327:0.557691:0.561327:0.541978:0.552344:0.541978:0.000000 S D:@0.575648:0.558273:0.591110:0.558273:0.591110:0.540619:0.575648:0.540619:0.000000:0.000000:0.000000 5 2:@0.594257:0.557136:0.628071:0.557136:0.628071:0.543420:0.594257:0.543420:0.000000:0.000000:0.000000 S D:@0.651080:0.558273:0.666543:0.558273:0.666543:0.540619:0.651080:0.540619:0.000000:0.000000:0.000000 5:@0.669690:0.557136:0.685023:0.557136:0.685023:0.543420:0.669690:0.543420:0.000000 1:@0.690316:0.548580:0.695955:0.548580:0.695955:0.532154:0.690316:0.532154:0.000000 x:@0.690316:0.564964:0.698110:0.564964:0.698110:0.548827:0.690316:0.548827:0.000000 entonces,:@0.711471:0.557691:0.781901:0.557691:0.781901:0.541978:0.711471:0.541978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S DS D:@0.515545:0.592472:0.552819:0.592472:0.552819:0.574818:0.515545:0.574818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg x f x g x x :@0.519539:0.591890:0.666668:0.591890:0.666668:0.576454:0.519539:0.576454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.555967:0.591335:0.571300:0.591335:0.571300:0.577619:0.555967:0.577619:0.000000 S D S D:@0.579086:0.592472:0.619104:0.592472:0.619104:0.574818:0.579086:0.574818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.622251:0.591335:0.656065:0.591335:0.656065:0.577619:0.622251:0.577619:0.000000:0.000000:0.000000 1:@0.672343:0.582753:0.681734:0.582753:0.681734:0.566326:0.672343:0.566326:0.000000 x:@0.672343:0.599136:0.680136:0.599136:0.680136:0.582999:0.672343:0.582999:0.000000 :@0.689525:0.591891:0.711327:0.591891:0.711327:0.576455:0.689525:0.576455:0.000000:0.000000:0.000000 5 2:@0.692773:0.591336:0.726587:0.591336:0.726587:0.577620:0.692773:0.577620:0.000000:0.000000:0.000000 1:@0.726495:0.591891:0.731888:0.591891:0.731888:0.576178:0.726495:0.576178:0.000000 .:@0.731815:0.591891:0.735146:0.591891:0.735146:0.576455:0.731815:0.576455:0.000000 Si :@0.479175:0.634064:0.499405:0.634064:0.499405:0.618351:0.479175:0.618351:0.000000:0.000000:0.000000:0.000000 x , f x , g x x ,:@0.499294:0.634064:0.722288:0.634063:0.722288:0.618627:0.499294:0.618629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 $:@0.506676:0.633509:0.522009:0.633509:0.522009:0.619794:0.506676:0.619794:0.000000 0:@0.525156:0.634064:0.534139:0.634064:0.534139:0.618351:0.525156:0.618351:0.000000 S D:@0.548460:0.634646:0.563922:0.634646:0.563922:0.616992:0.548460:0.616992:0.000000:0.000000:0.000000 5:@0.567070:0.633509:0.582403:0.633509:0.582403:0.619794:0.567070:0.619794:0.000000 2:@0.585551:0.634064:0.593245:0.634064:0.593245:0.618351:0.585551:0.618351:0.000000 S D:@0.608873:0.634646:0.624335:0.634646:0.624335:0.616992:0.608873:0.616992:0.000000:0.000000:0.000000 5 2:@0.627482:0.633509:0.661296:0.633509:0.661296:0.619794:0.627482:0.619794:0.000000:0.000000:0.000000 1:@0.666640:0.623564:0.676031:0.623564:0.676031:0.607138:0.666640:0.607138:0.000000 2:@0.666640:0.639948:0.676031:0.639948:0.676031:0.623521:0.666640:0.623521:0.000000 2:@0.695156:0.633508:0.710489:0.633508:0.710489:0.619792:0.695156:0.619792:0.000000 1 luego :@0.713637:0.634063:0.775559:0.634063:0.775559:0.618350:0.713637:0.618350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.722214:0.625243:0.725528:0.625243:0.725528:0.609807:0.722214:0.609807:0.000000 :@0.478374:0.679897:0.482405:0.679897:0.482405:0.664184:0.478374:0.664184:0.000000 S DS D:@0.482331:0.680480:0.519606:0.680480:0.519606:0.662825:0.482331:0.662825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg x f x g x :@0.486326:0.679897:0.618453:0.679897:0.618453:0.664462:0.486326:0.664462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.522753:0.679342:0.538087:0.679342:0.538087:0.665627:0.522753:0.665627:0.000000 S D S D:@0.545873:0.680480:0.585890:0.680480:0.585890:0.662825:0.545873:0.662825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.589038:0.679342:0.604371:0.679342:0.604371:0.665627:0.589038:0.665627:0.000000 2:@0.607519:0.679897:0.615213:0.679897:0.615213:0.664184:0.607519:0.664184:0.000000 2:@0.619922:0.683674:0.635952:0.683674:0.635952:0.669335:0.619922:0.669335:0.000000 x :@0.635856:0.684254:0.670588:0.684254:0.670588:0.668117:0.635856:0.668117:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.645921:0.673598:0.651559:0.673598:0.651559:0.657171:0.645921:0.657171:0.000000 2:@0.644727:0.693562:0.652771:0.693562:0.652771:0.677135:0.644727:0.677135:0.000000 2:@0.670530:0.683674:0.686560:0.683674:0.686560:0.669335:0.670530:0.669335:0.000000 1:@0.686464:0.684254:0.692103:0.684254:0.692103:0.667827:0.686464:0.667827:0.000000 x .:@0.695246:0.679897:0.772281:0.679897:0.772281:0.664462:0.695246:0.664462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2 2:@0.698486:0.679342:0.758181:0.679342:0.758181:0.665627:0.698486:0.665627:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.761328:0.679897:0.769022:0.679897:0.769022:0.664184:0.761328:0.664184:0.000000 Así, :@0.494368:0.724040:0.522634:0.724040:0.522634:0.708327:0.494368:0.708327:0.000000:0.000000:0.000000:0.000000:0.000000 S D S D:@0.522539:0.725334:0.564324:0.725334:0.564324:0.707680:0.522539:0.707680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg x :@0.526534:0.724752:0.567545:0.724752:0.567545:0.709317:0.526534:0.709317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.567471:0.724197:0.582805:0.724197:0.582805:0.710482:0.567471:0.710482:0.000000 2:@0.600929:0.713096:0.616959:0.713096:0.616959:0.698757:0.600929:0.698757:0.000000 1,:@0.616863:0.713676:0.625773:0.713676:0.625773:0.697249:0.616863:0.697249:0.000000:0.000000 x ,:@0.625677:0.713676:0.689660:0.713676:0.689660:0.697539:0.625677:0.697539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si:@0.629075:0.713519:0.639715:0.713519:0.639715:0.697806:0.629075:0.697806:0.000000:0.000000 #:@0.657542:0.713096:0.673572:0.713096:0.673572:0.698757:0.657542:0.698757:0.000000 0:@0.676863:0.713676:0.686254:0.713676:0.686254:0.697249:0.676863:0.697249:0.000000 2:@0.600929:0.741084:0.616262:0.741084:0.616262:0.727368:0.600929:0.727368:0.000000 :@0.616170:0.741638:0.619484:0.741638:0.619484:0.726203:0.616170:0.726203:0.000000 x , x .:@0.619417:0.741796:0.729959:0.741796:0.729959:0.725659:0.619417:0.725659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.630540:0.741216:0.646570:0.741216:0.646570:0.726877:0.630540:0.726877:0.000000 2:@0.649861:0.741796:0.659252:0.741796:0.659252:0.725369:0.649861:0.725369:0.000000 si:@0.669374:0.741638:0.680013:0.741638:0.680013:0.725926:0.669374:0.725926:0.000000:0.000000 $:@0.697841:0.741216:0.713871:0.741216:0.713871:0.726877:0.697841:0.726877:0.000000 0:@0.717162:0.741796:0.726553:0.741796:0.726553:0.725369:0.717162:0.725369:0.000000 En la Figura 6.4 se representan las funciones :@0.336350:0.763904:0.657341:0.763904:0.657341:0.748192:0.336350:0.748192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g:@0.656875:0.763904:0.676330:0.763904:0.676330:0.748469:0.656875:0.748469:0.000000:0.000000:0.000000:0.000000 y . Identifica a cada una de ellas.:@0.676258:0.763904:0.926891:0.763904:0.926891:0.748192:0.676258:0.748192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg:@0.698421:0.763904:0.712300:0.763904:0.712300:0.748469:0.698421:0.748469:0.000000:0.000000 6.5 Demostración:@0.336350:0.791266:0.474955:0.791266:0.474955:0.774319:0.336350:0.774319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Se demuestra la propiedad conmutativa del producto de funciones. El resto se deja :@0.336350:0.818809:0.930562:0.818809:0.930562:0.803096:0.336350:0.803096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como tarea para el estudiante.:@0.336350:0.835450:0.555742:0.835450:0.555742:0.819738:0.336350:0.819738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Sean :@0.336350:0.862815:0.393495:0.862815:0.393495:0.847102:0.336350:0.847102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g F A .:@0.393392:0.862815:0.463984:0.862815:0.463984:0.847380:0.393392:0.847380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.416383:0.862676:0.431716:0.862676:0.431716:0.848628:0.416383:0.848628:0.000000 S D:@0.442853:0.863397:0.460744:0.863397:0.460744:0.845743:0.442853:0.845743:0.000000:0.000000:0.000000 Entonces, para cada :@0.463910:0.862815:0.616477:0.862815:0.616477:0.847102:0.463910:0.847102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.616267:0.862815:0.626962:0.862815:0.626962:0.847380:0.616267:0.847380:0.000000:0.000000 [ :@0.626907:0.862676:0.646750:0.862676:0.646750:0.848628:0.626907:0.848628:0.000000:0.000000 A:@0.646658:0.862815:0.656542:0.862815:0.656542:0.847380:0.646658:0.847380:0.000000 se tiene: :@0.656469:0.862815:0.728183:0.862815:0.728183:0.847102:0.656469:0.847102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x , g x :@0.355308:0.884824:0.428164:0.884824:0.428164:0.869388:0.355308:0.869388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S D S D:@0.359928:0.885406:0.406461:0.885406:0.406461:0.867752:0.359928:0.867752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.409609:0.884685:0.424942:0.884685:0.424942:0.870636:0.409609:0.870636:0.000000 R:@0.428090:0.883964:0.441380:0.883964:0.441380:0.871066:0.428090:0.871066:0.000000 y:@0.441288:0.884824:0.457302:0.884824:0.457302:0.869111:0.441288:0.869111:0.000000:0.000000:0.000000 f x g x g x f x . :@0.457210:0.884824:0.584368:0.884824:0.584368:0.869388:0.457210:0.869388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S D S D:@0.468328:0.885406:0.508346:0.885406:0.508346:0.867752:0.468328:0.867752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.511493:0.884269:0.526826:0.884269:0.526826:0.870553:0.511493:0.870553:0.000000 S D S D:@0.539178:0.885406:0.577888:0.885406:0.577888:0.867752:0.539178:0.867752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Luego, :@0.584312:0.884824:0.637276:0.884824:0.637276:0.869111:0.584312:0.869111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S DS D:@0.477845:0.912768:0.515119:0.912768:0.515119:0.895114:0.477845:0.895114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg x f x g x g x f x gf x , x A,:@0.481839:0.912186:0.785293:0.912179:0.785293:0.896743:0.481839:0.896750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.518267:0.911631:0.533600:0.911631:0.533600:0.897915:0.518267:0.897915:0.000000 S D S D:@0.541387:0.912768:0.581404:0.912768:0.581404:0.895114:0.541387:0.895114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.584552:0.911631:0.599885:0.911631:0.599885:0.897915:0.584552:0.897915:0.000000 S D S D:@0.615476:0.912768:0.654186:0.912768:0.654186:0.895114:0.615476:0.895114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.657334:0.911631:0.672667:0.911631:0.672667:0.897915:0.657334:0.897915:0.000000 S DS D:@0.675815:0.912768:0.713089:0.912768:0.713089:0.895114:0.675815:0.895114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.753669:0.912040:0.769002:0.912040:0.769002:0.897992:0.753669:0.897992:0.000000 y por la igualdad de funciones se concluye que :@0.355299:0.939541:0.700246:0.939541:0.700246:0.923828:0.355299:0.923828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fg gf:@0.699846:0.939541:0.749270:0.939541:0.749270:0.924105:0.699846:0.924105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.716910:0.938986:0.732243:0.938986:0.732243:0.925270:0.716910:0.925270:0.000000 .:@0.749215:0.939541:0.752417:0.939541:0.752417:0.923828:0.749215:0.923828:0.000000 x:@0.291709:0.636035:0.297206:0.636035:0.297206:0.624103:0.291709:0.624103:0.000000 y:@0.113611:0.468741:0.119285:0.468741:0.119285:0.456809:0.113611:0.456809:0.000000 4:@0.110594:0.499004:0.116637:0.499004:0.116637:0.487072:0.110594:0.487072:0.000000 3:@0.110594:0.531552:0.116637:0.531552:0.116637:0.519620:0.110594:0.519620:0.000000 2:@0.110594:0.564100:0.116637:0.564100:0.116637:0.552168:0.110594:0.552168:0.000000 1:@0.110594:0.596649:0.116637:0.596649:0.116637:0.584717:0.110594:0.584717:0.000000 0:@0.115901:0.634521:0.121944:0.634521:0.121944:0.622589:0.115901:0.622589:0.000000 1:@0.165691:0.638611:0.171734:0.638611:0.171734:0.626679:0.165691:0.626679:0.000000 2:@0.208660:0.638611:0.214703:0.638611:0.214703:0.626679:0.208660:0.626679:0.000000 3:@0.251630:0.638611:0.257673:0.638611:0.257673:0.626679:0.251630:0.626679:0.000000 y = 2x:@0.162704:0.514609:0.193861:0.514609:0.193861:0.502677:0.162704:0.502677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = x:@0.214759:0.515843:0.255150:0.515843:0.255150:0.503910:0.214759:0.503910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.255145:0.511219:0.258669:0.511219:0.258669:0.504262:0.255145:0.504262:0.000000 1:@0.236957:0.511166:0.241873:0.511166:0.241873:0.501459:0.236957:0.501459:0.000000 2:@0.236957:0.519451:0.241873:0.519451:0.241873:0.509745:0.236957:0.509745:0.000000 1:@0.145475:0.631499:0.148969:0.631499:0.148969:0.624600:0.145475:0.624600:0.000000 2:@0.145475:0.637387:0.148969:0.637387:0.148969:0.630489:0.145475:0.630489:0.000000 1:@0.115642:0.603620:0.119135:0.603620:0.119135:0.596721:0.115642:0.596721:0.000000 2:@0.115642:0.609508:0.119135:0.609508:0.119135:0.602610:0.115642:0.602610:0.000000 1:@0.115732:0.615479:0.119050:0.615479:0.119050:0.608928:0.115732:0.608928:0.000000 4:@0.115732:0.621065:0.119050:0.621065:0.119050:0.614514:0.115732:0.614514:0.000000 y = x:@0.214850:0.593991:0.255242:0.593991:0.255242:0.582059:0.214850:0.582059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.255241:0.589364:0.258764:0.589364:0.258764:0.582407:0.255241:0.582407:0.000000 1:@0.237019:0.589648:0.242008:0.589648:0.242008:0.579798:0.237019:0.579798:0.000000 4:@0.237019:0.598055:0.242008:0.598055:0.242008:0.588206:0.237019:0.588206:0.000000 –3:@0.100319:0.828066:0.107529:0.828408:0.108069:0.821940:0.100860:0.821598:0.000000:0.000000 –2:@0.122119:0.838891:0.129343:0.838891:0.129343:0.832410:0.122119:0.832410:0.000000:0.000000 –1:@0.145911:0.838891:0.153135:0.838891:0.153135:0.832410:0.145911:0.832410:0.000000:0.000000 0:@0.168984:0.836619:0.172266:0.836619:0.172266:0.830138:0.168984:0.830138:0.000000 1:@0.195887:0.838891:0.199170:0.838891:0.199170:0.832410:0.195887:0.832410:0.000000 3:@0.166680:0.780171:0.169962:0.780171:0.169962:0.773690:0.166680:0.773690:0.000000 2:@0.166680:0.797755:0.169962:0.797755:0.169962:0.791274:0.166680:0.791274:0.000000 1:@0.166680:0.815339:0.169962:0.815339:0.169962:0.808858:0.166680:0.808858:0.000000 –1:@0.179802:0.850653:0.187026:0.850653:0.187026:0.844172:0.179802:0.844172:0.000000:0.000000 –2:@0.179802:0.868238:0.187026:0.868238:0.187026:0.861756:0.179802:0.861756:0.000000:0.000000 –3:@0.179802:0.885822:0.187026:0.885822:0.187026:0.879341:0.179802:0.879341:0.000000:0.000000 –4:@0.179802:0.903406:0.187026:0.903406:0.187026:0.896925:0.179802:0.896925:0.000000:0.000000 2:@0.219227:0.838902:0.222510:0.838902:0.222510:0.832421:0.219227:0.832421:0.000000 3:@0.242567:0.838902:0.245849:0.838902:0.245849:0.832421:0.242567:0.832421:0.000000 x:@0.279451:0.836630:0.282437:0.836630:0.282437:0.830149:0.279451:0.830149:0.000000 y:@0.166783:0.763647:0.169865:0.763647:0.169865:0.757166:0.166783:0.757166:0.000000 (2, –2):@0.223744:0.865876:0.241809:0.865876:0.241809:0.859395:0.223744:0.859395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (2, –4):@0.205636:0.912081:0.223700:0.912081:0.223700:0.905600:0.205636:0.905600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = – x– 1:@0.254560:0.874562:0.291950:0.874564:0.291950:0.868083:0.254560:0.868081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.282099:0.872050:0.283066:0.872050:0.283066:0.868272:0.282099:0.868272:0.000000 1:@0.272786:0.872204:0.275496:0.872204:0.275496:0.866854:0.272786:0.866854:0.000000 2:@0.272786:0.876770:0.275496:0.876770:0.275496:0.871420:0.272786:0.871420:0.000000 y = –x – 2:@0.230135:0.904009:0.258261:0.904009:0.258261:0.897527:0.230135:0.897527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = :@0.149150:0.899046:0.169763:0.899046:0.169763:0.892565:0.149150:0.892565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.161292:0.896688:0.164001:0.896688:0.164001:0.891338:0.161292:0.891338:0.000000 x:@0.161414:0.901255:0.163879:0.901255:0.163879:0.895905:0.161414:0.895905:0.000000 y = 2:@0.247214:0.792681:0.261151:0.792681:0.261151:0.786200:0.247214:0.786200:0.000000:0.000000:0.000000:0.000000:0.000000 y = –x:@0.125329:0.790203:0.142911:0.790203:0.142911:0.783721:0.125329:0.783721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (2, 2):@0.222355:0.803226:0.236477:0.803226:0.236477:0.796745:0.222355:0.796745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = –1:@0.087444:0.854706:0.105323:0.854706:0.105323:0.848225:0.087444:0.848225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 6.3:@0.249078:0.676984:0.300402:0.676984:0.300402:0.665556:0.249078:0.665556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 6.4:@0.249076:0.940005:0.300402:0.940005:0.300402:0.928578:0.249076:0.928578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El producto de funciones :@0.082576:0.181885:0.248321:0.181885:0.248321:0.167601:0.082576:0.167601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cumple con las :@0.082576:0.197014:0.184201:0.197014:0.184201:0.182730:0.082576:0.182730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 propiedades::@0.082576:0.212143:0.166809:0.212143:0.166809:0.197859:0.082576:0.197859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Conmutativa:@0.082576:0.226358:0.181873:0.226358:0.181873:0.211961:0.082576:0.211961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Para todo :@0.181766:0.226358:0.253971:0.226358:0.253971:0.212788:0.181766:0.212788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g F A , fg gf.:@0.096806:0.247919:0.215047:0.247919:0.215047:0.233186:0.096806:0.233186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.118751:0.247484:0.131994:0.247484:0.131994:0.235351:0.118751:0.235351:0.000000 S D:@0.142105:0.248475:0.159183:0.248475:0.159183:0.231623:0.142105:0.231623:0.000000:0.000000:0.000000 5:@0.181603:0.247390:0.196240:0.247390:0.196240:0.234297:0.181603:0.234297:0.000000 2. Asociativa:@0.082576:0.267337:0.163559:0.267337:0.163559:0.252941:0.082576:0.252941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Para todo:@0.163456:0.267337:0.229543:0.267337:0.229543:0.253767:0.163456:0.253767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f g h:@0.096799:0.287075:0.129134:0.287075:0.129134:0.273745:0.096799:0.273745:0.000000:0.000000:0.000000:0.000000:0.000000 , , F , :@0.100789:0.287075:0.177890:0.287075:0.177890:0.273505:0.100789:0.273505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.132488:0.286956:0.145730:0.286956:0.145730:0.274823:0.132488:0.274823:0.000000 1 2 1:@0.156334:0.287578:0.185330:0.287578:0.185330:0.272332:0.156334:0.272332:0.000000:0.000000:0.000000:0.000000:0.000000 A f gh:@0.159783:0.287075:0.201386:0.287075:0.201386:0.273745:0.159783:0.273745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.201339:0.287578:0.204868:0.287578:0.204868:0.272332:0.201339:0.272332:0.000000 :@0.204788:0.287075:0.224850:0.287075:0.224850:0.273505:0.204788:0.273505:0.000000:0.000000:0.000000 5:@0.208206:0.286596:0.221448:0.286596:0.221448:0.274751:0.208206:0.274751:0.000000 1 2:@0.224787:0.287578:0.243705:0.287578:0.243705:0.272332:0.224787:0.272332:0.000000:0.000000:0.000000 fg h:@0.228237:0.287075:0.251828:0.287075:0.251828:0.273745:0.228237:0.273745:0.000000:0.000000:0.000000:0.000000 .:@0.251764:0.287075:0.254530:0.287075:0.254530:0.273505:0.251764:0.273505:0.000000 3.:@0.082539:0.306814:0.093921:0.306814:0.093921:0.292417:0.082539:0.292417:0.000000:0.000000 Existencia de :@0.093886:0.306804:0.188047:0.306804:0.188047:0.293234:0.093886:0.293234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 elemento :@0.190136:0.306804:0.259071:0.306804:0.259071:0.292407:0.190136:0.292407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 unidad.:@0.096804:0.322685:0.147929:0.322685:0.147929:0.308289:0.096804:0.308289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.148104:0.322685:0.151395:0.322685:0.151395:0.308049:0.148104:0.308049:0.000000 Existe :@0.152794:0.322685:0.193424:0.322685:0.193424:0.309115:0.152794:0.309115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.194889:0.322685:0.203045:0.322685:0.203045:0.308289:0.194889:0.308289:0.000000 A :@0.203240:0.326033:0.210687:0.326033:0.210687:0.317443:0.203240:0.317443:0.000000:0.000000 [:@0.211468:0.322569:0.224711:0.322569:0.224711:0.310436:0.211468:0.310436:0.000000 F A ,:@0.224927:0.323004:0.255729:0.323004:0.255729:0.308270:0.224927:0.308270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S D:@0.236225:0.323560:0.252829:0.323560:0.252829:0.306708:0.236225:0.306708:0.000000:0.000000:0.000000 :@0.255713:0.322689:0.259194:0.322689:0.259194:0.309119:0.255713:0.309119:0.000000 definida como :@0.096805:0.338571:0.211847:0.338574:0.211847:0.325004:0.096805:0.325001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.194604:0.338571:0.202759:0.338571:0.202759:0.324174:0.194604:0.324174:0.000000 A:@0.202830:0.341918:0.208331:0.341918:0.208331:0.333329:0.202830:0.333329:0.000000 S D:@0.212588:0.339446:0.227119:0.339446:0.227119:0.322594:0.212588:0.322594:0.000000:0.000000:0.000000 x 1,:@0.216576:0.338890:0.255706:0.338890:0.255706:0.324156:0.216576:0.324156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.229983:0.338360:0.244619:0.338360:0.244619:0.325268:0.229983:0.325268:0.000000 :@0.255713:0.338574:0.259194:0.338574:0.259194:0.325004:0.255713:0.325004:0.000000:0.000000:0.000000:0.000000 ;:@0.096806:0.355506:0.108526:0.355506:0.108526:0.342414:0.096806:0.342414:0.000000 x A, :@0.109176:0.356036:0.166046:0.356036:0.166046:0.341302:0.109176:0.341302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.129273:0.354340:0.142516:0.354340:0.142516:0.342207:0.129273:0.342207:0.000000 tal que para :@0.169165:0.354460:0.259191:0.354460:0.259191:0.340890:0.169165:0.340890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 todo :@0.096801:0.370341:0.138217:0.370345:0.138217:0.356775:0.096801:0.356771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f F A , f f .:@0.130319:0.370660:0.236864:0.370660:0.236864:0.355927:0.130319:0.355927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.138153:0.370225:0.151395:0.370225:0.151395:0.358093:0.138153:0.358093:0.000000 S D:@0.160974:0.371216:0.176998:0.371216:0.176998:0.354365:0.160974:0.354365:0.000000:0.000000:0.000000 1:@0.186692:0.370345:0.194847:0.370345:0.194847:0.355949:0.186692:0.355949:0.000000 A:@0.194780:0.373689:0.200280:0.373689:0.200280:0.365099:0.194780:0.365099:0.000000 :@0.200243:0.370345:0.203725:0.370345:0.203725:0.356775:0.200243:0.356775:0.000000 5:@0.210648:0.370131:0.225285:0.370131:0.225285:0.357039:0.210648:0.357039:0.000000 4. Distributiva.:@0.082576:0.390078:0.176218:0.390078:0.176218:0.375682:0.082576:0.375682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.176098:0.390078:0.179389:0.390078:0.179389:0.375442:0.176098:0.375442:0.000000 Para todo:@0.179325:0.390078:0.239292:0.390078:0.239292:0.376508:0.179325:0.376508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g, h F A ,:@0.096806:0.411640:0.175834:0.411640:0.175834:0.396906:0.096806:0.396906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.133725:0.411356:0.147664:0.411356:0.147664:0.398585:0.133725:0.398585:0.000000 S D:@0.157244:0.412196:0.173268:0.412196:0.173268:0.395344:0.157244:0.395344:0.000000:0.000000:0.000000 f g h fg fh.:@0.096801:0.427525:0.218056:0.427525:0.218056:0.412791:0.096801:0.412791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.104321:0.428081:0.108222:0.428081:0.108222:0.411229:0.104321:0.411229:0.000000 1:@0.120012:0.426995:0.134648:0.426995:0.134648:0.413903:0.120012:0.413903:0.000000 D:@0.146666:0.428081:0.150567:0.428081:0.150567:0.411229:0.146666:0.411229:0.000000 5:@0.153572:0.426995:0.168208:0.426995:0.168208:0.413903:0.153572:0.413903:0.000000 1:@0.185937:0.426995:0.200573:0.426995:0.200573:0.413903:0.185937:0.413903:0.000000 Competencia :@0.078581:0.138603:0.187141:0.138603:0.187141:0.121656:0.078581:0.121656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.155244:0.176057:0.155244:0.176057:0.138297:0.078581:0.138297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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