So I have an input function $f(t)$ and an output function $h(t)$ such that,
$g(f(t)) = h(t)$
I was wondering if anyone knew of any numerical methods to find $g$ or its inverse?
More explicitly I have a function,
$f(V(t)) = \frac{|\zeta(t)|^2}{\int_t^\infty |\zeta(s)|^2 ds}$
$V(t)$ and $\zeta(t)$ are known and stored so calculating $f(V(t))$ isn't hard. What I want to know is given an arbitrary $\zeta(t)$ what should $V(t)$ be? For that I need to know $f^{-1}$.
Any help is appreciated.