Thread: Function equation, two unknown functions of x

1. Function equation, two unknown functions of x

Hi there. I didn't know where to post this, so I postet it here.

Two functions $\displaystyle f(x)$ and $\displaystyle g(x)$ are such that

$\displaystyle f(g(x))^{-1}=\frac{f(x)}{2x}$

$\displaystyle g(f(x))=2\cdot f(g(x))$