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.

Question

Kristian

Mathematics

20 February, 04:52

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.

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Answers (1)

Know the Answer?

Delaney Hartman · 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)