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Given the following functions, evaluate each of the following: f(x) = x² + 7x + 10 g(x) = x + 2 (ƒ + g)(9): (ƒ − g)(9) = (f. g)(9) = (9) = =

Given the following functions, evaluate each of the following: f(x) = x² + 7x + 10 g(x) = x + 2 (ƒ + g)(9): (ƒ − g)(9) = (f. g)(9) = (9) = =

Calculus: Early Transcendentals
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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### 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.
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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