Question

Let n be a nonzero integer. find a domain on which f (x) = (1 − xn)1/n coincides with its inverse. hint: the answer depends on whether n is even or odd.

Answer 1

I believe that the correct equation given is:

f(x) = (1-x^n)^(1/n)

From this, we can say that:

When n is an odd number then f(x) is cubic root function. The domain is (-infinite, +finite)
When n is an even number then f(x) is sqrt root function. The domain is (0, +finite)