Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Section 2.5 - Introduction to Relations and Functions - 2.5 Exercises - Page 195: 59


$y \text{ is a function of }x \\\text{Domain: } \left[ -\dfrac{1}{2},\infty \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To determine if the given equation, $ y=\sqrt{4x+2} ,$ is a function, check if $x$ is unique for every value of $y.$ To find the domain, find the set of all possible values of $x.$ $\bf{\text{Solution Details:}}$ For each value of $x,$ multiplying it by $4$ and then adding $2$ will produce a single value of $y.$ Hence, $y$ is a function of $x.$ The radicand, $4x+2,$ of a radical with an even index cannot be negative. Hence, \begin{array}{l}\require{cancel} 4x+2\ge0 \\\\ 4x\ge-2 \\\\ \dfrac{4x}{4}\ge-\dfrac{2}{4} \\\\ x\ge-\dfrac{1}{2} .\end{array} The given equation has the following characteristics: \begin{array}{l}\require{cancel} y \text{ is a function of }x \\\text{Domain: } \left[ -\dfrac{1}{2},\infty \right) .\end{array}
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