Question

Determine the values of n

Answer 1

b. n is odd

Explanation:

In this problem, we assume that
`n` is a whole number. The definition of inverse functions tells us that a function
`f` has an inverse function if and only if the function is one-to-one, that is, if there is no any horizontal line intersecting the graph of
`f` at more than one point. This only happens if
`n` is odd. This is called the Horizontal Line Test for Inverse Functions. So let's take two examples:

FIRST:

`n=2 \\ \\ f(x)=x^2`

Since n is even, an horizontal line will pass through two points as indicated in the first figure below.

SECOND:

`n=3 \\ \\ f(x)=x^3`

Since n is odd, an horizontal line will pass through just one point as indicated in the second figure below.