If \sqrt w denotes the principal branch of square root of w, for w in \{0}, then what is the maximal open set in which f(z)=\sqrt{z^3 -1} defines an analytic function and compute f^{-1}(3).

The maximal open set in which f is analytic is z=r exp(i ), for r>1 and - /3< < /3 ?

Thanks.