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 229: 65


$h$ doesn't have an inverse.

Work Step by Step

We are given the function: $h(x)=|x+1|-1$ Graph the function using a set of points: $x=-3\Rightarrow h(-3)=|-3+1|-1=1$ $x=-2\Rightarrow h(-2)=|-2+1|-1=0$ $x=-1\Rightarrow h(-1)=|-1+1|-1=-1$ $x=0\Rightarrow h(0)=|0+1|-1=0$ $x=1\Rightarrow h(1)=|1+1|-1=1$ Graph the function. Perform the Horizontal Line Test. The test fails as there are horizontal lines which intersect the graph at more than one point. Therefore, the function doesn't have an inverse.
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