What is the inverse function of f(x)=?
Thanks.
Actually, that has a very simple answer. The inverse function to $\displaystyle f(x)= xe^x$ is, by definition, $\displaystyle f^{-1}(x)= W(x)$, "Lambert's W function". It cannot be written in terms of elementary functions.
See http://en.wikipedia.org/wiki/Lambert's_W_function