Composite function simple question

Question

Can you help me with an example?

I have to find a composite function that answers:

1) Define a function $f$ and a function $g$ such that $f (g(x)) = f (x) g (x)$.

I tried to find functions that are derived, but it did not work. (I know the trivial examples of $f(x)=1=g(x)$ and $f(x)=0$, and I am looking for more interesting examples.)

Answer 1

Let $f(x)=x^2$ and $g(x)=x^2$.