what is this concept/function called? When you find a "proxy function" $g(x)$ whose roots coincide with those of $f(x)$ so that its extrema coincide and serves as an inverse?
I'm not sure if I described that correctly, but I have some function analytic function
$f(x)$ and I want to know at what point f(x) takes its minimum or maximum. I found a function $g(x)$ that I derived from f(x) by using Maple's solve command.. and it returned the function $g(x)$ inside the "RootOf" command which says that the inverse of $f(x)$ can be found by finding the root of $g(x)$