Inverse Functions

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• October 2nd 2008, 11:39 AM
uclabruins00
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.
• October 2nd 2008, 01:22 PM
Opalg
Quote:

Originally Posted by uclabruins00
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.