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 February 22nd, 2014, 12:40 PM #1 Senior Member   Joined: Jan 2014 Posts: 196 Thanks: 3 Text Example Inverse Function The purpose of this example in the text is to show that $f^{-1}$ of $z^2$ is the principle sqrt function $z^{1/2}$ We have $z=re^{i\theta}$ and $w=\rho e^{i\phi}$ Suppose that $w=f^{-1}(z)$ Since the range of $f^{-1}$ is the domain of $f$ , the principal argument $\phi$ of $w$ must satisfy $-\pi/2 < \phi \leq \pi/2$. This part I am not understanding. I am thinking that the principal argument $\phi$ of $w$ would be the domain of $f^{-1}$, and could be another interval as long as it is mapped to $-\pi/2 < \phi \leq \pi/2$. Some help explaining this further, or in a different way for me? Thanks!

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