Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 230: 91

Answer

False statement

Work Step by Step

We have to check if the following statement is true: "If $f$ is an even function, then $f^{-1}$ exists." Consider the function: $f(x)=x^2$ Check if the function is even: $f(-x)=(-x)^2=x^2=f(x)\checkmark$ Graph the function and use the Horizontal Line Test. The test fails, so the function doesn't have an inverse. This shows that the given statement is FALSE.
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