Exercise 8, Sec. 111 of Complex Variables and Applications (9th ed.) asks:
Corresponding to the each point on the Riemann surface for $w=f(z)=[z(z^2-1)]^{1/2}$, it can be shown there is only one value of $w$. Show that corresponding to each value of $w$, there are in general, three points on the surface.
Since $f$ is surjective, I have tried creating a function $g$ such that $g(w)=z_1,z_2,z_3$. Another method I tried was letting $z$ rotate around all the branch points in a circuit but I just do not know how to proceed. I really appreciate any help or comment as I am struggling to grasp Riemann surfaces.