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Chapter 6: Q. 81 (page 411)

find (f鈭�g)(x)and (g鈭�f)(x)and graph each of these functions.

role="math" localid="1646571519431" f(x)=sinxg(x)=4x

Short Answer

Expert verified

If f(x)=sinx&g(x)=4xthen (f鈭�g)(x)=sin(4x)and (g鈭�f)(x)=4sin(x)their graph is

Step by step solution

01

Step 1. Given data

The given functions are

f(x)=sinxg(x)=4x

02

Step 2. compositions of functions

Composition (f鈭�g)(x)is

role="math" localid="1646571446110" (f鈭�g)(x)=f(g(x))=f(4x)=sin(4x)

03

Step 3. composition of functions

Composition (g鈭�f)(x)is

role="math" localid="1646571470462" (g鈭�f)(x)=g(f(x))=g(sin(x))=4sin(x)

04

Step 4. Graph of the composition of functions

Plot the graph of (f鈭�g)(x)=sin(4x)and(g鈭�f)(x)=4sin(x)

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