Question

f:R−R,f(x)=3x+7.Sa se determine functia g:R−R, stiind ca (g°f) (x)=−6x−5, oricare ar fi x apartine lui R

Answer 1

g(x)=ax+b    <- am scris forma generala a functiei de gradul 1

(g°f)(x)=g(f(x))=af(x)+b=a(3x+7)+b=3ax+7a+b
dar (g°f)(x)=-6x-5

=> 3ax+7a+b=-6x-5                 am egalat termenii asemenea
3a=-6 => a=-2
7a+b=-5 => 7*(-2)+b=-5
                   -14+b=-5 => b=9

=> g(x)=-2x+9