College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Review Exercises - Page 279: 120

Answer

$(f+g)(1)=8$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the value of the given expression, $ (f+g)(1) ,$ use the definition of the appropriate function operation. Then substitute the values in the given table. $\bf{\text{Solution Details:}}$ Using $(f+g)(x)=f(x)+g(x),$ then \begin{array}{l}\require{cancel} (f+g)(1)=f(1)+g(1) \text{ (Equation *)} .\end{array} Based on the given table, when $x= 1 ,$ the value of $f(x)$ is $ 7 .$ Hence, $ f(1)=7 .$ Based on the given table, when $x= 1 ,$ the value of $g(x)$ is $ 1 .$ Hence, $ g(1)=1 .$ By substitution, Equation * becomes \begin{array}{l}\require{cancel} (f+g)(1)=f(1)+g(1) \\\\ (f+g)(1)=7+1 \\\\ (f+g)(1)=8 .\end{array}
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