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Invertible Functions and Local Inverses

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See the attached function and answer the following questions:
(a) Is f invertible?
(b) In which points does f have a local inverse?
(c) Determine the derivative of the local inverse at f((-1,1)) and f((1,-1))

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https://brainmass.com/math/geometry-and-topology/invertible-functions-local-inverses-602262

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The solution gives details on determining if a function is invertible and has a local inverse and finding the derivative of local inverse at given points.

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