Suppose you have some data which roughly follows the form $(x_n, f(g(x_n)))$, where regression models are known for $f$ and $g$ individually. Is there a known way to generate a regression model for the given dataset?
This is more of a general question, thus I have no example data. But to provide an example, suppose you have any set of data. Then say you have some function $f$:
$$f(x)=ae^{bx^2+cx+d}$$
This can be viewed as the composition of two functions:
$$ \begin{align} f(x)&=g(h(x))\mathrm{,\,where}\\ g(x)&=ae^x\\ h(x)&=bx^2+cx+d \end{align} $$
There are known methods for performing a regressions to $g$ and $h$ individually. My question is, since it's possible to perform a regression to $g$ and $h$ individually, are there known methods for performing a regression to $f(x)$?