Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![### Given the following functions, evaluate each of the following:
#### Functions:
\[ f(x) = x^2 + 7x + 10 \]
\[ g(x) = x + 2 \]
### Tasks:
Evaluate the following expressions for \( x = 9 \):
1. \((f + g)(9) = \) (Enter your answer here)
2. \((f - g)(9) = \) (Enter your answer here)
3. \((f \cdot g)(9) = \) (Enter your answer here)
4. \(\left(\frac{f}{g}\right)(9) = \) (Enter your answer here)
### Steps for Evaluation:
1. **Addition of Functions \( (f + g) \):**
\[ (f + g)(x) = f(x) + g(x) \]
Substitute \( x = 9 \).
2. **Subtraction of Functions \( (f - g) \):**
\[ (f - g)(x) = f(x) - g(x) \]
Substitute \( x = 9 \).
3. **Multiplication of Functions \( (f \cdot g) \):**
\[ (f \cdot g)(x) = f(x) \cdot g(x) \]
Substitute \( x = 9 \).
4. **Division of Functions \( \left(\frac{f}{g}\right) \):**
\[ \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} \]
Substitute \( x = 9 \).
### Notes:
- Ensure all computations adhere to order of operations (PEMDAS/BODMAS).
- For division, verify that \( g(x) \neq 0 \) to avoid division by zero errors.
Please calculate the results and enter them into the provided spaces.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90d1e96e-989a-4849-aeb9-585c1e797a4d%2Fcaf0bf7d-0ef2-4166-82c1-aee64dc279a4%2F84obx1_processed.png&w=3840&q=75)
Transcribed Image Text:### Given the following functions, evaluate each of the following:
#### Functions:
\[ f(x) = x^2 + 7x + 10 \]
\[ g(x) = x + 2 \]
### Tasks:
Evaluate the following expressions for \( x = 9 \):
1. \((f + g)(9) = \) (Enter your answer here)
2. \((f - g)(9) = \) (Enter your answer here)
3. \((f \cdot g)(9) = \) (Enter your answer here)
4. \(\left(\frac{f}{g}\right)(9) = \) (Enter your answer here)
### Steps for Evaluation:
1. **Addition of Functions \( (f + g) \):**
\[ (f + g)(x) = f(x) + g(x) \]
Substitute \( x = 9 \).
2. **Subtraction of Functions \( (f - g) \):**
\[ (f - g)(x) = f(x) - g(x) \]
Substitute \( x = 9 \).
3. **Multiplication of Functions \( (f \cdot g) \):**
\[ (f \cdot g)(x) = f(x) \cdot g(x) \]
Substitute \( x = 9 \).
4. **Division of Functions \( \left(\frac{f}{g}\right) \):**
\[ \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} \]
Substitute \( x = 9 \).
### Notes:
- Ensure all computations adhere to order of operations (PEMDAS/BODMAS).
- For division, verify that \( g(x) \neq 0 \) to avoid division by zero errors.
Please calculate the results and enter them into the provided spaces.
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