Question

Fie functia f:R->R ,f(x)=3x+7.Sa se determine functia g:R->R stiind ca (g○f)(x)=-6x-5.

Answer 1

$f(x) = 3x+7 \\ (g*f)(x) = -6x -5 \\ (g*f)(x)=g(f(x))=g(3x+7)=-6x-5 \\ Not:\ 3x+7=t \\ 3x=t-7 \\ x= \frac{t-7}{3} \\ g(3x+7)=g(t)=-6\cdot \frac{t-7}{3}-5 \\ g(t)=-2t+14-5 \\ g(t)=-2t+9 \\ Deci,\ revenind\ la\ variabila\ x\ avem:\\ g(x)=-2x+9$