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: 87



Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given function, $ f(x)=\sqrt{3-x} ,$ 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} 3-x\ge0 \\\\ -x\ge-3 .\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} -x\ge-3 \\\\ \dfrac{-x}{-1}\ge\dfrac{-3}{-1} \\\\ x\le3 .\end{array} Hence the domain is $ (-\infty,3] .$
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