Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.1 Radical Expressions and Functions - 10.1 Exercise Set - Page 635: 102


$\left(-\infty,\dfrac{5}{7} \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given function, $ d(x)=-\sqrt[4]{5-7x} ,$ is the permissible values of $x.$ $\bf{\text{Solution Details:}}$ With an even index (index equals $ 4 $), then the radicand should be a nonnegative number. Hence, \begin{array}{l}\require{cancel} 5-7x\ge0 \\\\ -7x\ge-5 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol) the inequality above is equivalent to \begin{array}{l}\require{cancel} -7x\ge-5 \\\\ x\le\dfrac{-5}{-7} \\\\ x\le\dfrac{5}{7} .\end{array} Hence, the domain is the interval $ \left(-\infty,\dfrac{5}{7} \right] .$
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.