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Practice problem

Domain of Inverse Function

By Amy Feraco
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The inverse of f(x)=tan⁡(x)f(x)=\tan{(x)} is f−1(x)=arctan⁡(x)f^{-1}(x)=\arctan{(x)} or f−1(x)=tan⁡−1(x)f^{-1}(x)=\tan^{-1}{(x)}.

What is the range of the inverse if the domain of f(x)=tan⁡(x)f(x)=\tan{(x)} is (−π2,π2)(-\frac{\pi}{2},\frac{\pi}{2}) and the range is (−∞,∞)(-\infty,\infty)?

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