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: 22

Answer

No, r(t) is not one-to-one.

Work Step by Step

The function $r(t)=t^4-1$ 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 $t$ values: $f(-1)=(-1)^4-1=1-1=0$ $f(1)=1^4-1=1-1=0$ Thus the function is not one-to-one.
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