(1) Let $\displaystyle f$ be a one-to-one analytic function on a domain $\displaystyle D$ and suppose that there is an analytic function $\displaystyle h$ on $\displaystyle D$ with $\displaystyle h^2 = f$. Show that $\displaystyle h$ is also one-to-one.

Not really important but if anyone could help me out, I would appreciate it, thanks!