Question

if h(x)=(fog)(x) and h(x) = x+5, find g(x) if f(x) = x+2

Answer 1

$\bf \begin{cases} f(x)=x+2\\ h(x)=x+5\\ h(x)=(f\circ g)(x) \end{cases}\quad (f\circ g)(x)\implies \stackrel{h(x)}{f(~g(x)~)} \\\\\\ \stackrel{h(x)}{f(~~g(x)~~)}=g(x)+2=\stackrel{h(x)}{x+5}\implies g(x)+2=x+5 \\\\\\ g(x)=x+5-2\implies \boxed{g(x)=x+3}$