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: 32

Answer

$p(4)=\text{does not exist} ,\\\\ p(10)=0 ,\\\\ p(12)=2 ,\\\\ p(0)=\text{does not exist}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Substitute the given function value in $ p(z)=\sqrt{2z-20} .$ $\bf{\text{Solution Details:}}$ If $ z=4 ,$ then \begin{array}{l}\require{cancel} p(z)=\sqrt{2z-20} \\\\ p(4)=\sqrt{2(4)-20} \\\\ p(4)=\sqrt{-12} \text{ (not a real number)} .\end{array} If $ z=10 ,$ then \begin{array}{l}\require{cancel} p(z)=\sqrt{2z-20} \\\\ p(10)=\sqrt{2(10)-20} \\\\ p(10)=\sqrt{0} \\\\ p(10)=0 .\end{array} If $ z=12 ,$ then \begin{array}{l}\require{cancel} p(z)=\sqrt{2z-20} \\\\ p(12)=\sqrt{2(12)-20} \\\\ p(12)=\sqrt{4} \\\\ p(12)=2 .\end{array} If $ z=0 ,$ then \begin{array}{l}\require{cancel} p(z)=\sqrt{2z-20} \\\\ p(0)=\sqrt{2(0)-20} \\\\ p(0)=\sqrt{-20} \text{ (not a real number)} .\end{array} Hence, \begin{array}{l}\require{cancel} p(4)=\text{does not exist} ,\\\\ p(10)=0 ,\\\\ p(12)=2 ,\\\\ p(0)=\text{does not exist} .\end{array}
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