College Algebra (11th Edition)

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

Chapter 2 - Section 2.8 - Function Operations and Composition - 2.8 Exercises - Page 269: 55

Answer

$(f\circ g)(2)=1$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To evaluate the given expression, $ (f\circ g)(2) ,$ use the definition of function composition. Use the given table for the values of the function. $\bf{\text{Solution Details:}}$ Since $(f\circ g)(x)=f(g(x)),$ then \begin{array}{l}\require{cancel} (f\circ g)(2)=f(g(2)) .\end{array} Based on the table, the value of $ g $ when $x= 2 $ is $ 3 .$ Hence, $ g(2)=3 .$ By substitution, the equation above becomes \begin{array}{l}\require{cancel} (f\circ g)(2)=f(g(2)) \\\\ (f\circ g)(2)=f(3) .\end{array} Based on the table, the value of $ f $ when $x= 3 $ is $ 1 .$ Hence, $ f(3)=1 .$ By substitution, the equation above becomes \begin{array}{l}\require{cancel} (f\circ g)(2)=f(g(2)) \\\\ (f\circ g)(2)=f(3) \\\\ (f\circ g)(2)=1 .\end{array}
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