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Chapter 10: Q. 359 (page 1061)

For functions

fx=2x3+5and

g(x)=3x2-7,find

(a)f鈭�g(-1)(b)g鈭�f(-2)(c)g鈭�g(1)

Short Answer

Expert verified

The answers are

(a)f鈭�g(-1)=-123(b)g鈭�f(-2)=356(c)g鈭�g(1)=41

Step by step solution

01

Step 1. Given information

The given pair of functions are

fx=2x3+5and

g(x)=3x2-7

02

Step 2. Part (a) Find the value of f∘g-1

f鈭�g(-1)=fg-1=f3-12-7=f3-7=f(-4)=2-43+5=-128+5=-123

03

Step 3. Part (b) Find the value of g∘f(-2)

g鈭�f(-2)=gf-2=g2-23+5=g-16+5=g-11=3-112-7=363-7=356

04

Step 4. Part(c) Find the value of g∘g(1)

g鈭�g(1)=gg1=g312-7=g3-7=g-4=3-42-7=48-7=41

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Most popular questions from this chapter

On the same coordinate system, graph:

f(x)=3x

g(x)=3x+1

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

Convert from exponential to logarithmic form:

ex=6.

In the following exercises, graph each logarithmic function.

y=log6x

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