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: 18


$h(x)$ is one-to-one.

Work Step by Step

The function $h(x)=x^3+8$ is one-to-one because it passes the horizontal line test (a shifted $x^3$ graph). We can show this algebraically: We start with the assumption that: $x_1\ne x_2$ Then: ${x_1}^3\ne {x_2}^3$ (Since cubing a unique number results in a unique value.) ${x_1}^3+8\ne {x_2}^3+8$ So the function would not have the same $y$ value for two different $x$ values (one-to-one).
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