# Proving theorem connecting the inverse of a holomorphic function to a contour integral of the function.

I am asked to prove this theorem:

If $f:U \rightarrow C$ is holomorphic in $U$ and invertible, $P\in U$ and if $D(P,r)$ is a sufficently small disc about P, then

$$f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds$$

The book says to "imitate the proof of the argument principle" but I am not seeing the connection.

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