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Chapter 6: Q. 84 (page 411)

find (f鈭�g)(x)and (g鈭�f)(x)and graph each of these functions.
role="math" localid="1646574749097" f(x)=-3xg(x)=sinx

Short Answer

Expert verified

If f(x)=-3xandg(x)=sinxthen (g鈭�f)(x)=-sin(3x)and(f鈭�g)(x)=-3sin(x)and their graph is

Step by step solution

01

Step 1. Given data 

The given functions are

f(x)=-3xg(x)=sinx

02

Step 2. compositions of functions 

Composition (f鈭�g)(x)is

(f鈭�g)(x)=f(g(x))=f(sin(x))=-3sinx

03

Step 3. compositions of functions 

Composition (g鈭�f)(x)is

(g鈭�f)(x)=g(f(x))=g(-3x)=sin(-3x)=-sin(3x)

04

Step 4. Graph of the composition of functions 

Plot the graph of (f鈭�g)(x)=-3sin(x)and(g鈭�f)(x)=-sin(3x)

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