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BaLLatris [955]
2 years ago
6

Determine the values of n

Mathematics
1 answer:
N76 [4]2 years ago
8 0
<h2>Answer:</h2><h3>b. n is odd</h3><h2>Step-by-step explanation:</h2>

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.

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