Answer:
b. n is odd
Step-by-step explanation:
In this problem, we assume that [tex]n[/tex] is a whole number. The definition of inverse functions tells us that a function [tex]f[/tex] 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 [tex]f[/tex] at more than one point. This only happens if [tex]n[/tex] is odd. This is called the Horizontal Line Test for Inverse Functions. So let's take two examples:
FIRST:
[tex]n=2 \\ \\ f(x)=x^2[/tex]
Since n is even, an horizontal line will pass through two points as indicated in the first figure below.
SECOND:
[tex]n=3 \\ \\ f(x)=x^3[/tex]
Since n is odd, an horizontal line will pass through just one point as indicated in the second figure below.
