Question 4
Let $c$ be a rational. Let $f(x) = x^2 + c$. Define $f^{(0)}(x) = x$, $f^{(n+1)}(x) = f(f^{(n)}(x))$. Show that there are only finitely many rationals $x$ such that the sequence $f^{(0)}(x), f^{(1)}(x), f^{(2)}(x), \dots$ takes only finitely many values.