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: 21


Yes, r(t) is one-to-one.

Work Step by Step

The function $r(t)=t^6-3$, $0\leq t\leq 5$ is one-to-one because it passes the horizontal line test on the given interval (the graph is an even function, but the interval only spans one side of it). We can show this algebraically: We start with the assumption that: $t_1\ne t_2$ Then: ${t_1}^6\ne {t_2}^6$ (Since raising a unique positive number to the 6th power results in a unique value.) ${t_1}^6-3\ne {t_2}^6-3$ So the function would not have the same $y$ value for two different $t$ values (one-to-one).
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.