Find functions f and g such that F = f ∘ g.

Question

Find functions f and g such that F = f ∘ g.  (Use non-identity functions for f(x)  and g(x).)

Answer 1

This question can have multiple answers.

F = f º g = f(g(x)), where we substitute g(x) for x in f(x)

Given the equation for F(x), f(x) can be x/(6+x), and g(x) can be cuberoot(x).

Another option is that f(x) = cuberoot(x)/(6+cuberoot(x)) and g(x) = x.

One trick to solving similar problems is to look for the variable and get f(x) and g(x) accordingly.