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Chapter 10: Q. 6 (page 1002)

In the following exercises, find

a.f鈭�g(x)

b.g鈭�f(x)

c.(f.g)(x)

Short Answer

Expert verified

The composition is6x2-2,12x2-1,6x3-2xrespectively

Step by step solution

01

Given information

Given the function

f(x)=2xg(x)=3x2-1

02

Use the composition and calculate

Using composition, we get

f鈭�g(x)=f[g(x)]f鈭�g(x)=f(3x2-1)f鈭�g(x)=2(3x2-1)f鈭�g(x)=6x2-2

03

Use the composition and calculate

Using composition and calculate, we get

g鈭�f(x)=g[f(x)]g鈭�f(x)=g(2x)g鈭�f(x)=3(2x)2-1 g鈭�f(x)=12x2-1

04

Use the composition and calculate

Using composition, we get

(f路g)(x)=f(x)路g(x)(f路g)(x)=(2x)路3x2-1(f.g)(x)=2x路3x2-2x路1(f.g)(x)=6x3-2x

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