= Solution
The identity $w-1=-2/(z+1)$ gives $\boxed{|w-1|=2/r}$ on $|z+1|=r$. Thus the image circle has center one and <radius> $2/r$. Points strictly inside the original circle satisfy $|w-1|>2/r$; the center itself maps to infinity. The interior therefore becomes the exterior together with infinity on the <Riemann sphere>, rather than the interior of the image circle. This inversion is a useful warning against assuming conformality preserves global inside/outside assignments.
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