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Chapter 6: Q. 82 (page 411)

find (f鈭�g)(x)and (g鈭�f)(x)and graph each of these functions.
role="math" localid="1646572889893" f(x)=cosxg(x)=12x

Short Answer

Expert verified

If f(x)=cosx&g(x)=12xthen(g鈭�f)(x)=12cos(x)&(f鈭�g)(x)=cos12x and their graph is

Step by step solution

01

Step 1. Given data 

The given functions are

f(x)=cosxg(x)=12x

02

Step 2. compositions of functions 

Composition(f鈭�g)(x)is

(f鈭�g)(x)=f(g(x))=f12x=cos12x

03

Step 3. compositions of functions 

Composition (g鈭�f)(x)is

(g鈭�f)(x)=g(f(x))=g(cos(x))=12cosx

04

Step 4. Graph of the composition of functions 

Plot the graph of(f鈭�g)(x)=cos12xand(g鈭�f)(x)=12cosx

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