Let $U$ be an open subset of $\mathbb{C}$ containing $\{z\in\mathbb{C}\mid |z|\leq 1\}$ and let $f:U\to\mathbb{C}$ be the map defined by $f(z)=e^{i\omega}(z-a)/(1-\overline{a}z)$ for $a\in D$ and $\omega\in [0,2\pi]$.
Which of the following are true?
(a) $|f(e^{i\theta})|=1$ for $0≤\theta≤ 2\pi $
(b) $f$ maps $\{z\in\mathbb{C}\mid|z|\leq1\}$ onto itself
(c) $f$ maps $\{z\in\mathbb{C}\mid|z|\leq 1\}$ into itself
(d) $f$ is one-one
How should I able to solve this problem. Can anyone help me please