College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 262: 23


No, f(x) is not one-to-one.

Work Step by Step

The function $f(x)=\frac{1}{x^2}$ is not one-to-one because it fails the horizontal line test (even function). We can show that it has the same $y$ value for two different $x$ values: $f(-1)=\frac{1}{(-1)^2}=\frac{1}{1}=1$ $f(1)=\frac{1}{(1)^2}=\frac{1}{1}=1$ Thus the function is not one-to-one.
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