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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 $g(x)$

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  • $\begingroup$ it might help if you gave a reference. I have occasionally seen the phrase "proxy function" but I have no idea what it means. Hmmm, the first page of things on Google is all about computer programming. $\endgroup$ – Will Jagy Feb 1 '18 at 20:02
  • $\begingroup$ I updated the article with my specific example, but the concept is a general one not tied to this specific analytic function definition $\endgroup$ – crow Feb 2 '18 at 0:48
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Oh, duh, the answer is Adjoint operator, also known as the dual or conjugate operator. It is a Normal operator and also a Unitary operator

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