I tried posting this at stack exchange but it never got the question answered. I want to prove this:
If f:U→C is holomorphic in U and invertible, P∈U and if D(P,r) is a sufficently small disc about P, then
f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds