# Composing functions

Algebra Level 5

Consider all pairs of polynomials $$f(x)$$ and $$g(x)$$ such that $\begin{cases} f(g(x)) =f(x)+g(x), \\ f(0) = 5, \\ f(1) = 7, \\ g(0) \neq 0.\\ \end{cases}$ What are the last three digits of the sum of all (distinct) possible values of $$f(20)?$$

Details and assumptions

The empty sum (sum of no elements) is 0.

×