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: 123

Answer

$[-3,2)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given function, $ f(x)=\dfrac{\sqrt{x+3}}{\sqrt[4]{2-x}} ,$ are the combined restrictions of the numerator and the denominator. $\bf{\text{Solution Details:}}$ In the numerator, since the radicand of a radical with an even index (index equals $2$), should be nonnegative, then \begin{array}{l}\require{cancel} x+3\ge0 \\\\ x\ge-3 .\end{array} In the denominator, since the radicand of a radical with an even index (index equals $4$), should be nonnegative, and that the denominator cannot be zero, then \begin{array}{l}\require{cancel} 2-x\gt0 \\\\ -x\gt-2 \\\\ x\lt\dfrac{-2}{-1} \\\\ x\lt2 .\end{array} Combining the two restrictions above, then the domain is the interval $ [-3,2) .$
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