Refer to the functions r and p. Find the function (p-r) (x) and write the domain in interval notation. r(x) = 4x p(x)=x²+2x 9(x) = √7-x Part: 0/2 Part 1 of 2 (p-r)(x) = 0/6 010
Refer to the functions r and p. Find the function (p-r) (x) and write the domain in interval notation. r(x) = 4x p(x)=x²+2x 9(x) = √7-x Part: 0/2 Part 1 of 2 (p-r)(x) = 0/6 010
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.CR: Review Problem Set
Problem 24CR: An outpatient operating room charges each patient a fixed amount per surgery plus an amount per...
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![### Functions and Domain
#### Problem Statement
Refer to the functions \( r \) and \( p \). Find the function \( (p-r)(x) \) and write the domain in interval notation.
Given functions:
\[ r(x) = 4x \]
\[ p(x) = x^2 + 2x \]
\[ q(x) = \sqrt{7-x} \]
#### Solution
**Part 1: Calculating \( (p-r)(x) \)**
To find \( (p-r)(x) \):
\[ (p-r)(x) = p(x) - r(x) \]
Given:
\[ p(x) = x^2 + 2x \]
\[ r(x) = 4x \]
So,
\[ (p-r)(x) = (x^2 + 2x) - 4x \]
\[ (p-r)(x) = x^2 + 2x - 4x \]
\[ (p-r)(x) = x^2 - 2x \]
**Part 2: Domain Determination**
To find the domain of \( (p-r)(x) \), consider the domains of the original functions \( r(x) \) and \( p(x) \). Both functions are polynomials, which are defined for all real numbers.
Hence, the domain of \( (p-r)(x) = x^2 - 2x \) is:
\[ (-\infty, \infty) \]
#### Answer Summary:
- \( (p-r)(x) = x^2 - 2x \)
- Domain of \( (p-r)(x) \): \( (-\infty, \infty) \)
#### Graphical and Diagram Explanation
There are no specific graphs or diagrams provided in the image. The problem is purely algebraic.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F262a59b3-3740-48a2-981b-c8dd0f86c255%2Ffd246373-0c44-42d0-b42d-e2e0485ac143%2F79q3m2e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Functions and Domain
#### Problem Statement
Refer to the functions \( r \) and \( p \). Find the function \( (p-r)(x) \) and write the domain in interval notation.
Given functions:
\[ r(x) = 4x \]
\[ p(x) = x^2 + 2x \]
\[ q(x) = \sqrt{7-x} \]
#### Solution
**Part 1: Calculating \( (p-r)(x) \)**
To find \( (p-r)(x) \):
\[ (p-r)(x) = p(x) - r(x) \]
Given:
\[ p(x) = x^2 + 2x \]
\[ r(x) = 4x \]
So,
\[ (p-r)(x) = (x^2 + 2x) - 4x \]
\[ (p-r)(x) = x^2 + 2x - 4x \]
\[ (p-r)(x) = x^2 - 2x \]
**Part 2: Domain Determination**
To find the domain of \( (p-r)(x) \), consider the domains of the original functions \( r(x) \) and \( p(x) \). Both functions are polynomials, which are defined for all real numbers.
Hence, the domain of \( (p-r)(x) = x^2 - 2x \) is:
\[ (-\infty, \infty) \]
#### Answer Summary:
- \( (p-r)(x) = x^2 - 2x \)
- Domain of \( (p-r)(x) \): \( (-\infty, \infty) \)
#### Graphical and Diagram Explanation
There are no specific graphs or diagrams provided in the image. The problem is purely algebraic.
![Refer to the functions \( r, p, \) and \( q \). Find the function \( (p \cdot q)(x) \) and write the domain in interval notation.
Given functions:
\[ r(x) = -3x \]
\[ p(x) = x^2 - 4x \]
\[ q(x) = \sqrt{7 - x} \]
*There are no graphs or diagrams present in the image.*
**Part: 0 / 2**
**Part 1 of 2**
\[ (p \cdot q)(x) = \]
[There is an empty field here for entering the function.]
[Below the empty field, there are buttons with icons for different mathematical expressions and operations. The options appear to include basic arithmetic operations, exponents, roots, and possibly formatting options like subscript and superscript. Below this panel, there are 'X' and 'refresh' buttons, likely for clearing or resetting the input field.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F262a59b3-3740-48a2-981b-c8dd0f86c255%2Ffd246373-0c44-42d0-b42d-e2e0485ac143%2Fg55ltar_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Refer to the functions \( r, p, \) and \( q \). Find the function \( (p \cdot q)(x) \) and write the domain in interval notation.
Given functions:
\[ r(x) = -3x \]
\[ p(x) = x^2 - 4x \]
\[ q(x) = \sqrt{7 - x} \]
*There are no graphs or diagrams present in the image.*
**Part: 0 / 2**
**Part 1 of 2**
\[ (p \cdot q)(x) = \]
[There is an empty field here for entering the function.]
[Below the empty field, there are buttons with icons for different mathematical expressions and operations. The options appear to include basic arithmetic operations, exponents, roots, and possibly formatting options like subscript and superscript. Below this panel, there are 'X' and 'refresh' buttons, likely for clearing or resetting the input field.]
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