Doua functii f:M->N si g:X->Y sunt egale daca si numai daca M=X, N=Y si legile lor sunt egale ( f(x)=g(x) pentru orice x din M)
[tex]Trebuie~sa~avem:~ \\ \\ A= \{-1;3;7;10 \}~si~ \left \{ {{2=1-n} \atop {m-3=11}} \right. \Leftrightarrow \left \{ {{n=3} \atop {m=14}} \right. . \\ \\ Deci~f(x)=g(x)=2x+11. \\ \\ f(-1)=9~;~f(3)=17~;~f(7)=25~;~f(10)=31. \\ \\ Deci~f~devine~ \\ \\ \boxed{f:\{-1;3;7;10\} \rightarrow \{9;17;25;31 \},~f(x)=2x+11}. \\ \\ Si~din~ceea~ce~am~spus~in~primele~randuri,~rezulta \\ \\ \boxed{ B= \{9;17;25;31 \} }.[/tex]
[tex]Ce~pot~sa~spun?~Cerinta~este~aiurea... \\ \\ Trebuia~ceruta~multimea~B~cu~numar~MINIM~de~elemente.~ \\ \\ De~ce?~Pentru~ca~B~putea~fi~ORICE~multime~care~contine~ \\ \\ elementele~9,~17,~25,~31. \\ \\ Puteam~avea~B=R,~B=Q,~B=Z,~B=N,~ \\ \\ B= \{9,17,25,31,a_1,a_2... \},~(functia~ramanand~aceeasi~~ \\ \\ deoarece~domeniul~ramane~acelasi). [/tex]
