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 9 - Inequalities and Problem Solving - 9.2 Intersections, Unions, and Compound Inequalities - 9.2 Exercise Set - Page 591: 90


$\left(-\infty, \dfrac{8}{5} \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given function, $ f(x)=\sqrt{8-5x} ,$ is all values of $x$ for which the radicand is non-negative. Express the answer in interval notation. $\bf{\text{Solution Details:}}$ Since the radicand of a radical with an even index has to be non-negative, then \begin{array}{l}\require{cancel} 8-5x\ge0 \\\\ -5x\ge-8 .\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} -5x\ge-8 \\\\ x\ge\dfrac{-8}{-5} \\\\ x\le\dfrac{8}{5} .\end{array} Hence the domain is $ \left(-\infty, \dfrac{8}{5} \right] .$
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