Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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I submitted all of these questions already and all of the answers I got (are in the pic) are incorrect. Please help correct all of them!!!
![**Unit 3 HW 2.3: The Algebra of Functions**
Let \( f(x) = x^2 + 5x \) and \( g(x) = 9 - x \).
Find
\[
\left( \frac{f}{g} \right)(x) \text{ and } \left( \frac{f}{g} \right)(8).
\]
\[
\left( \frac{f}{g} \right)(x) = 104 \quad (\text{Simplify your answer.})
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7df23386-bd9c-4b1d-ab26-cbe28cadafc2%2F65c1bff7-2069-4f84-b320-e6002bd8ddb6%2Flladmnl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Unit 3 HW 2.3: The Algebra of Functions**
Let \( f(x) = x^2 + 5x \) and \( g(x) = 9 - x \).
Find
\[
\left( \frac{f}{g} \right)(x) \text{ and } \left( \frac{f}{g} \right)(8).
\]
\[
\left( \frac{f}{g} \right)(x) = 104 \quad (\text{Simplify your answer.})
\]
![### The Algebra of Functions
Given two functions:
- \( f(x) = x^2 + 6x \)
- \( g(x) = 1 - x \)
We are tasked with finding:
- \( (f - g)(x) \)
- \( (f - g)(5) \)
#### Solution:
1. **Calculate \( (f - g)(x) \):**
\[
(f - g)(x) = f(x) - g(x)
\]
\[
= (x^2 + 6x) - (1 - x)
\]
\[
= x^2 + 6x - 1 + x
\]
\[
= x^2 + 7x - 1
\]
2. **Calculate \( (f - g)(5) \):**
Substitute \( x = 5 \) into \( (f - g)(x) \):
\[
(f - g)(5) = 5^2 + 7(5) - 1
\]
\[
= 25 + 35 - 1
\]
\[
= 59
\]
Thus, \( (f - g)(x) = x^2 + 7x - 1 \) and \( (f - g)(5) = 59 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7df23386-bd9c-4b1d-ab26-cbe28cadafc2%2F65c1bff7-2069-4f84-b320-e6002bd8ddb6%2Fytm7lq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### The Algebra of Functions
Given two functions:
- \( f(x) = x^2 + 6x \)
- \( g(x) = 1 - x \)
We are tasked with finding:
- \( (f - g)(x) \)
- \( (f - g)(5) \)
#### Solution:
1. **Calculate \( (f - g)(x) \):**
\[
(f - g)(x) = f(x) - g(x)
\]
\[
= (x^2 + 6x) - (1 - x)
\]
\[
= x^2 + 6x - 1 + x
\]
\[
= x^2 + 7x - 1
\]
2. **Calculate \( (f - g)(5) \):**
Substitute \( x = 5 \) into \( (f - g)(x) \):
\[
(f - g)(5) = 5^2 + 7(5) - 1
\]
\[
= 25 + 35 - 1
\]
\[
= 59
\]
Thus, \( (f - g)(x) = x^2 + 7x - 1 \) and \( (f - g)(5) = 59 \).
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