# real analysis – Distorted elementary functions

Let $$f(x)$$ be an elementary function defined on $$Xsubseteqmathbb{R}$$ and $$xi(x), eta(y)$$ strictly monotone for $$xin X,, yin f(x)$$.

Questions:

• is there an established name for functions of the form $$eta(f(xi(x)))$$, e.g. if $$f(x)$$ is a polynomial?
• are there classes of functions, say polynomials, that can be recognized from a distorted definition, resp., when is it possible to recover $$f(x)$$ from $$eta(f(xi(x)))$$ if the type (e.g. polynomial) of $$f(x)$$ is known?