2. Some approaches to the general problem

Extract

From any two given functions of x, f (x) and g(x), we can (if domain and range agree) construct their compositions f (g(x)) and g(f (x)). Thus from x²and tan x we construct (tan x)² and tan (x²). I started this investigation by wondering about the inverse situation, where, given a function h(x), we are interested in finding all possible pairs of functions f(x), g(x) whose composition f (g(x)) yields h(x).