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Math Help - Inverse Functions

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    Inverse Functions

    Let n be a non-zero integer. Find a domain on which f(x) = (1-x^n)^(1/n) coincides with its inverse. Hint: the answer depends on whether n is even or odd.
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    Quote Originally Posted by uclabruins00 View Post
    Let n be a non-zero integer. Find a domain on which f(x) = (1-x^n)^(1/n) coincides with its inverse. Hint: the answer depends on whether n is even or odd.
    Notice that f^{-1}(f(x)) = x. So if f coincides with its inverse then f(f(x)) = x. Calculate f(f(x)) and see where that leads you.
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