# Precalculus, Enhanced WebAssign Edition (6th Edition) View more editions Solutions for Chapter 4.FOM

• 7267 step-by-step solutions
• Solved by professors & experts
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Chapter: Problem:
Sample Solution
Chapter: Problem:
• Step 1 of 19

Consider

• Step 2 of 19

(a)

To find the domain of determine the values that would make the function undefined.

Because there are no values that make the function undefined, conclude that the domain of the function is.

• Step 3 of 19

(b)

To find the domain of we can determine the values that would make the function undefined.

Given function is a function with square root. The value under the radical is always positive.

Therefore, conclude that cannot less than -4. Because of this fact, conclude that the domain of the function is

• Step 4 of 19

(c)

To determine, simply plug -2 into as shown below:

• Step 5 of 19

To determine, simply plug 0 into as shown below:

• Step 6 of 19

To determine, simply plug 4 into as shown below:

• Step 7 of 19

To determine, simply plug 4 into as shown below:

• Step 8 of 19

To determine, simply plug 4 into as shown below:

• Step 9 of 19

To determine, we can simply plug 4 into as shown below:

Because the value under the radical is negative, the value of the function is undefined.

• Step 10 of 19

(d)

To determine, simply plug into as shown below:

To determine, simply plug into as shown below:

• Step 11 of 19

To determine, simply plug into as shown below:

• Step 12 of 19

(e)

The formula for the average rate of change is given below:

Average rate of change =

• Step 13 of 19

Using the equation above, we can solve for the rate of change as shown below:

• Step 14 of 19

First solve for and.

• Step 15 of 19

Using these values we can now solve for the average rate of change as shown below:

• Step 16 of 19

(f)

Find the composition of with. The value is as follows.

• Step 17 of 19

Similarly the composition ofwith is as follows.

• Step 18 of 19

Now find the values of

And

• Step 19 of 19

(g)

Consider

Let us assume that

The value under the radical is always positive. So,

Calculate the inverse as follows.

Squaring on both sides

Subtract 4 on both sides

It is noted that

Now interchange.

Therefore, the inverse of the function,

Corresponding Textbook

Precalculus, Enhanced WebAssign Edition | 6th Edition
9781133594765ISBN-13: 113359476XISBN: Authors:
Alternate ISBN: 9781133954750, 9781285499949
The text passage is a sample solution from a precalculus textbook, specifically addressing a problem that involves finding the domain of functions, evaluating functions at specific points, calculating the average rate of change, and finding the composition and inverse of functions.
no_question

the passage does not contain a mathematical question but rather provides a detailed solution to a problem, including multiple steps and calculations.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Precalculus, Enhanced WebAssign Edition (6th Edition) View more editions Solutions for Chapter 4.FOM

• 7267 step-by-step solutions
• Solved by professors & experts
• iOS, Android, & web
Chapter: Problem:
Sample Solution
Chapter: Problem:
• Step 1 of 19

Consider

• Step 2 of 19

(a)

To find the domain of determine the values that would make the function undefined.

Because there are no values that make the function undefined, conclude that the domain of the function is.

• Step 3 of 19

(b)

To find the domain of we can determine the values that would make the function undefined.

Given function is a function with square root. The value under the radical is always positive.

Therefore, conclude that cannot less than -4. Because of this fact, conclude that the domain of the function is

• Step 4 of 19

(c)

To determine, simply plug -2 into as shown below:

• Step 5 of 19

To determine, simply plug 0 into as shown below:

• Step 6 of 19

To determine, simply plug 4 into as shown below:

• Step 7 of 19

To determine, simply plug 4 into as shown below:

• Step 8 of 19

To determine, simply plug 4 into as shown below:

• Step 9 of 19

To determine, we can simply plug 4 into as shown below:

Because the value under the radical is negative, the value of the function is undefined.

• Step 10 of 19

(d)

To determine, simply plug into as shown below:

To determine, simply plug into as shown below:

• Step 11 of 19

To determine, simply plug into as shown below:

• Step 12 of 19

(e)

The formula for the average rate of change is given below:

Average rate of change =

• Step 13 of 19

Using the equation above, we can solve for the rate of change as shown below:

• Step 14 of 19

First solve for and.

• Step 15 of 19

Using these values we can now solve for the average rate of change as shown below:

• Step 16 of 19

(f)

Find the composition of with. The value is as follows.

• Step 17 of 19

Similarly the composition ofwith is as follows.

• Step 18 of 19

Now find the values of

And

• Step 19 of 19

(g)

Consider

Let us assume that

The value under the radical is always positive. So,

Calculate the inverse as follows.

Squaring on both sides

Subtract 4 on both sides

It is noted that

Now interchange.

Therefore, the inverse of the function,

Corresponding Textbook

Precalculus, Enhanced WebAssign Edition | 6th Edition
9781133594765ISBN-13: 113359476XISBN: Authors:
Alternate ISBN: 9781133954750, 9781285499949
user
The text passage is a sample solution from a precalculus textbook, specifically addressing a problem that involves finding the domain of functions, evaluating functions at specific points, calculating the average rate of change, and finding the composition and inverse of functions.

TYPE: NO_QUESTION

The passage does not contain a mathematical question but rather provides a detailed solution to a problem, including multiple steps and calculations.