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Chapter 5: Q. 1 (page 348)

Evaluate each expression using the graphs of y = f(x) and y = g(x) shown in the figure.

(a) (g o f)(-8)

(b) (fog)(-8)

(c) (g o g)(7)

(d) (g o f)(-5)

Short Answer

Expert verified

(a) -4

(b) 1

(c) -6

(d) -6

Step by step solution

01

Given Information 

Graph of two functions are given

02

Part(a) : Step (1) : composition of functions

(gof)(-8)g(f(-8))fromthegraphf(-8)f(-8)=2g(f(-8))=f(2)=-4g(f(-8))=-4

03

Part (b): Step 1: composition of function 

(fog)(-8)f(g(-8))fromthegraphg(-8)=-2f(g(-8))=f(-2)=1(fog)(-8)=1

04

Part(c) : Step 1 : composition of functions

(gog)(7)g(g(7))=g(0)=-6(gog)(7)=-6

05

Part(d): Step 1: composition of functions

(gof)(-5)g(f(-5))thevalueoff(-5)is4g(f(-5))=g(4)=-6(gof)(-5)=-6

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