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Chapter 10: Q. 2 (page 1002)

In the following exercises, find

a.f鈭�g(x)

b.g鈭�f(x)

c.(f.g)(x)

f(x)=3x-1g(x)=5x-3

Short Answer

Expert verified

The composition is15x-10,15x-8,15x2-14x+3respectively

Step by step solution

01

Given information

Given the function

f(x)=3x-1g(x)=5x-3

02

Use the composition and calculate

Using composition, we get

f鈭�g(x)=f(5x-3)f鈭�g(x)=3(5x-3)-1f鈭�g(x)=15x-9-1f鈭�g(x)=15x-10

03

Using composition and calculating

Using composition, we get

g鈭�f(x)=g[f(x)]g鈭�f(x)=g(3x-1)g鈭�f(x)=5(3x-1)-3g鈭�f(x)=15x-5-3g鈭�f(x)=15x-8

04

Using composition and calculate

Using composition, we get

(f路g)(x)=f(x)路g(x)(f路g)(x)=(3x-1)路(5x-3)(f路g)(x)=15x2-9x-5x+3(f路g)(x)=15x2-14x+3

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Most popular questions from this chapter

In the following exercises, find the inverse of each function.

f(x)=-5x-4

In the following exercises, graph, on the same coordinate system, the inverse of the one-to-one function shown.

In the following exercises, graph each exponential function.

f(x)=6x

In the following exercises, solve each logarithmic equation.y=log1.5x

Convert each logarithmic equation to exponential form:

3=log464.
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