Thread: 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.

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 . So if f coincides with its inverse then . Calculate f(f(x)) and see where that leads you.