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Chapter 6: Q. 48 (page 419)

find(f鈭�g)(x) and (g鈭�f)(x)and graph each of these functions.
role="math" localid="1646345864735" f(x)=12xg(x)=2cscx

Short Answer

Expert verified

If f(x)=12xand g(x)=2cscxthen (f鈭�g)(x)=csc(x)and its graph is

and (g鈭�f)(x)=2csc12xand its graph is

Step by step solution

01

Step 1. Given data

The given functions are

f(x)=12xg(x)=2cscx

02

Step 2. Composition of function 

(f鈭�g)(x)composition of function is

role="math" localid="1646346006367" (f鈭�g)(x)=f(g(x))(f鈭�g)(x)=f(2csc(x))(f鈭�g)(x)=12(2csc(x))(f鈭�g)(x)=csc(x)

03

Step 3. Graph of (f∘g)(x)

Plot the graph of (f鈭�g)(x)=csc(x)

04

Step 4. Composition of function 

(g鈭�f)(x)composition of function is

(g鈭�f)(x)=g(f(x))(g鈭�f)(x)=g12x(g鈭�f)(x)=2csc12x

05

Step 5. Graph of (g∘f)(x)

Plot the graph of (g鈭�f)(x)=2csc12x

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