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Chapter 6: Q. 83 (page 411)

find (f鈭�g)(x)and (g鈭�f)(x)and graph each of these functions.
role="math" localid="1646574166664" f(x)=-2xg(x)=cosx

Short Answer

Expert verified

Iff(x)=-2x&g(x)=cosxthen (g鈭�f)(x)=cos(-2x)and(f鈭�g)(x)=-2cosxand their graph is

Step by step solution

01

Step 1. Given data 

The given functions are

f(x)=-2xg(x)=cosx

02

Step 2. compositions of functions 

Composition (f鈭�g)(x)is

(f鈭�g)(x)=f(g(x))=f(cos(x))=-2cosx

03

Step 3. compositions of functions 

Composition(g鈭�f)(x)is

(g鈭�f)(x)=g(f(x))=g(-2x)=cos(-2x)

04

Step 4. Graph of the composition of functions 

Plot the graph of (f鈭�g)(x)=-2cosxand(g鈭�f)(x)=cos(-2x)

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