Let $g$ be a continuous function, really I'm interested to know more about functional equation, in particular the exponential function then it comes in my mind to solve the below functional in the case of $g$ real and complex valued , then my question here is:
Question: How do I solve this $\displaystyle g(g(x))=e^{-x²}$ for $g$ real valued and for $g$ a complex valued function ?