MathNet 1990 — Part 01 Question 6

Given that $f(x) = \frac{ax+b}{cx+d}$, $f(0) \neq 0$, $f(f(0)) \neq 0$. Let $F(x) = \underbrace{f(\dots(f(x)\dots))}_{n \text{ times}}$. If $F(0) = 0$, show that $F(x) = x$ for all $x$ where the expression is defined.