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: 89

Answer

$\left[ -\dfrac{7}{2},\infty \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given function, $ f(x)=\sqrt{2x+7} ,$ 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} 2x+7\ge0 \\\\ 2x\ge-7 \\\\ x\ge-\dfrac{7}{2} .\end{array} Hence the domain is $ \left[ -\dfrac{7}{2},\infty \right) .$
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