The function $f$ and the composite function $fg$ are defined as $f:x→x+2$ , $fg:x→3x-2$. Find the function g.

Question

The function $f$ and the composite function $fg$ are defined as $f:x\mapsto x+2$ , $fg:x\mapsto 3x-2$. Find the function $g$.

I just started learning functions and need help with it. Please provide workings so that I understand better, thank you.

Answer 1

$$f(x)=x+2 \rightarrow f(g(x))=g(x)+2 $$

but

$$f(g(x))=3x-2$$

so

$$g(x)+2=3x-2 \rightarrow g(x)=3x-4$$