Zeros of an Iterated Quadratic

Let $f_1(x)=f(x)=x(x-1)$ and $f_n(x)=f(f_{n-1}(x))$ for $n\geqslant 2$. Prove:

1. For $x>2$, $f_n(x)$ has no zeros. 2. For $1\leqslant x\leqslant 2$, $f_n(x)$ has at least $n$ zeros.