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: 58

Answer

$y \text{ is a function of }x \\\text{Domain: } [7,\infty)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To determine if the given equation, $ y=\sqrt{x-7} ,$ 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 $x,$ subtracting it by $7$ and getting the square root will produce a single value of $y.$ Hence, $y$ is a function of $x.$ The radicand, $x-7,$ of a radical with an even index cannot be negative. Hence, \begin{array}{l}\require{cancel} x-7\ge0 \\\\ x\ge7 .\end{array} The given equation has the following characteristics: \begin{array}{l}\require{cancel} y \text{ is a function of }x \\\text{Domain: } [7,\infty) .\end{array}
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