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Chapter 10: Q. 10 (page 1002)

For functions f(x)=5x2-1and

g(x)=4x-1find

a.f鈭�g(1)

b.g鈭�f(-1)

c.f鈭�f(2)

Short Answer

Expert verified

The value is 44,15,1804respectively

Step by step solution

01

Given information

Given the function

f(x)=5x2-1g(x)=4x-1

02

Calculate g(1) by substituting in g(x)

Substituting, x=1, we get

role="math" localid="1644935694008" g(1)=f(4x-1)g(1)=f(4(1)-1)g(1)=f(3)

03

Calculate f(3) by substituting in the function

Substituting , we get

f(3)=5x2-1f(3)=5(3)2-1f(3)=44

04

Calculate f(-1)  by substituting in the value

Substituting, we get

f(-1)=5(-1)2-1f(-1)=5-1f(-1)=4

05

Calculate g(4) by substituting the value in the function

Substituting the values, we get

g(4)=4x-1g(4)=4(4)-1g(4)=15g鈭�f(-1)=15

06

Step 6:Substitute f(2) by substituting in the values

Substituting, we get

f(2)=5x2-1f(2)=5(2)2-1f(2)=19

07

Calculating f(19) by substituting in the values 

Substituting the values, we get

f(19)=5x2-1f(19)=5(19)2-1f(19)=1804

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Most popular questions from this chapter

Verify that the functions are inverse functions.

f(x)=2x+6

g(x)=x-62

In the following exercises, solve each equation.

3x2-2x=13

In the following exercises, find

a.f鈭�g(x)

b.g鈭�f(x)

c.(f.g)(x)

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

鈸�2x鈸�2x+1鈸�2x-1鈸�2x+2鈸�2x鈭�2鈸�3x

In the following exercises, determine whether or not the given functions are inverses.
f(x)=x+8andg(x)=x-8
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