Finding Branch Points & Cuts for 3 Functions

[Matterwave]

Homework Statement

Find the branch points and introduce branch cuts for the below functions:

a) $$\frac{1}{4+\sqrt{z^2-9}}$$

b) $$\sqrt{4+\sqrt{z^2-9}$$

c) $$ln[5+\sqrt{\frac{z+1}{z-1}}]$$

Homework Equations

The Attempt at a Solution

So, the professor explained branches and branch cuts like they were completely obvious to him (which, they probably are...to him). He didn't show us basically at all how to find branching points and branch cuts except by giving us an example and finding it "obviously". Like he said the function f(z)=sqrt(z) branches at 0...but he never told us how we should find that point. I have no idea how to show where the branch points are...are they points where the function evaluates to 0 or something? Someone help?