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Chapter 10: Q. 5 (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 is6x2-9x,18x2-9x,6x3-9x2respectively

Step by step solution

01

Given information

Given the function

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

02

Use the composition and calculate

Using composition, we get

f鈭�g(x)=f[g(x)]f鈭�g(x)=f(2x2-3x)f鈭�g(x)=3(2x2-3x)f鈭�g(x)=6x2-9x

03

Use composition and calculate

Using composition, we get

g鈭�f(x)=g[f(x)]g鈭�f(x)=g(3x)g鈭�f(x)=2(3x)2-3(3x)g鈭�f(x)=18x2-9x

04

Use composition and calculate

Using composition, we get

(f.g)(x)=f(x).g(x)(f.g)(x)=(3x)路2x2-3x(f.g)(x)==3x路2x2-3x路3x(f.g)(x)=6x3-9x2

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Most popular questions from this chapter

Convert from exponential to logarithmic form:

4-3=164.

In the following exercises, solve each equation.

2x2+2x=12

In the following exercises, match the graphs to one of the following functions:

鈸�2x鈸�2x+1鈸�2x鈭�1鈸�2x+2鈸�2x鈭�2鈸�3x

The given graph is,

Graph: g(x)=5x

In the following exercises, solve each logarithmic equation.

y=log13x
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