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.
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 $\displaystyle f^{-1}(f(x)) = x$. So if f coincides with its inverse then $\displaystyle f(f(x)) = x$. Calculate f(f(x)) and see where that leads you.