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Chapter 5: Q 7. (page 256)

Evaluate each expression using the values given in the table.

(a)f∘g1(b)f∘g-1(c)g∘f-1(d)g∘f0(e)g∘g-2(f)f∘f-1

Short Answer

Expert verified

The value of (a) -1 (b) -1 (c) 8 (d) 0 (e) 8 (f) -7.

Step by step solution

01

Step 1. Given Information.

The evaluation of the functions are :

(a)f∘g1(b)f∘g-1(c)g∘f-1(d)g∘f0(e)g∘g-2(f)f∘f-1

02

Part (a) Step 1. Evaluation of a functional value.

The functional value

fg(1)=f0=-1.

03

Part (b) Step 1. Given Information.

The evaluation of the functions are :

(a)f∘g1(b)f∘g-1(c)g∘f-1(d)g∘f0(e)f∘f-1

04

Part (b) Step 2. Evaluation of a functional value. 

The value of the function is

fg-1=f0=-1.

05

Part (c) Step 1. Given Information. 

The evaluation of the functions are :

(a)f∘g1(b)f∘g-1(c)g∘f-1(d)g∘f0(e)f∘f-1

06

Part (c) Step 2. Evaluation of a given function. 

The functional value is

gf-1=g-3=8.

07

Part (d) Step 1. Given Information.

The evaluation of the functions are :

(a)f∘g1(b)f∘g-1(c)g∘f-1(d)g∘f0(e)f∘f-1

08

Part (d) Step 2. Evaluation of a given function. 

The value of the function is

gf0=g-1=0.

09

Part (e) Step 1. Given Information.

The evaluation of the functions are :

(a)f∘g1(b)f∘g-1(c)g∘f-1(d)g∘f0(e)f∘f-1

10

Part (e) Step 2. Evaluation of a given function.

The value of the function is

g∘g-2=gg-2=g3=8.

11

Part (f) Step 1. Given Information.

The evaluation of the given functions :

(a)f∘g1(b)f∘g-1(c)g∘f-1(d)g∘f0(e)f∘f-1.

12

Part (f) Step 2. Evaluation of a functional value.

The value of the function : f∘f-1=ff-1=f-3=-7.

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Most popular questions from this chapter

True or Falsefgx=fx.gx.

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

A(n)________ is a function of the form f(x)=Caxwhere a>0,a≠1,and C≠0are real numbers. The base ais a ____ and C is a _____.

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=2-e-x/2

Use the graph of y=f(x)given in the Problem 43to evaluate the following:

(a) f(-1)

(b) f(1)

(c) f-1(1)

(d) f-1(2)

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=ex-1
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