Let $U$ be an open and simply connected of $\mathbf{C}$ such that $0 \in U \neq \mathbf{C}$ and $U$ is symmetric about zero(that is, $z \in U \Leftrightarrow-z \in U$ ).
a) If $f: D \rightarrow U$ is a biholomorphism such that $f(0)=0$. Prove that $f(-z)=$ $-f(z)$ for all $z \in \mathbb{D}$.
b) Give an example of a holomorphic function $f: \mathbf{D} \longmapsto \mathbf{C}$ such that it is surjective.