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Determine the values of n for which f(x)=x^n has an inverse that is a function. Assume that n is a whole number. a. n is even c. n<0 b. n is odd d. n>0 Please select the best answer from the choices provided

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MrRoyal

The values of n for which f(x) = xⁿ has an inverse that is a function is (b) odd

How to determine the values of n?

From the question, we have the following parameters that can be used in our computation:

f(x) = x^n

Rewrite properly

So, we have

f(x) = xⁿ

Next, we calculate the inverse of the function

To start with, we replace the function notation f(x) with y

So, we have the following representation

y = xⁿ

Next, we swap the positions of x and y

This gives

x = yⁿ

Now, we make y the subject of the formula

Taking nth root on both sides, we get

x^1/n = y

So, we have

y = x^1/n

This represents the nth radical (x).

  • For an even radical we always get positive and negative values
  • But for an odd radical, the result is always a single value.

Therefore, n should be an odd whole number.

Hence, the values of n is (b) odd

Read more about inverse functions at

https://brainly.com/question/3831584

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