(This question might turn out to be too elementary for this site,
if so I'm sorry, but I can't find the answer anywhere.)
Does there exist a function $\; f : \{z\in \mathbb{C} : |z| < 1\} \to \mathbb{C} \;$
such that $f\hspace{.01 in}$ is a quasiconformal bijection and $f^{-1}$ is quasiconformal?
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