Help me please!

a)Let$\displaystyle f:B(a,r)\rightarrow B(f(a),R) $ be an analytical function/ Prove that $\displaystyle \forall z\in B(0,r)$$\displaystyle \left | f(z+a)-f(a) \right |\leqslant \frac{R}{r}\left | z \right |$.

b) Show that from a) we can get Liouville's theoremThanks a lot!