Find all holomorphic functions that satisfy a condition Find all holomorphic funtion $f:B(0,1)\mapsto B(1,4)$ s.t. $f(0)=3$ and $f(1/2)=1$

$B(a,r)$ is the open ball with centre a and radius r.

I think that maybe Schwarz lemma will help, but dont know how.
Thanks!
Try for example:
$$
f(z)=4\cdot\frac{2z-1}{z-2}+1
$$
which is also a bijection.
Try for example:
$$
f(z)=4\cdot\frac{2z-1}{z-2}+1
$$
which is also a bijection.