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Suppose f(x) = -x² - 4x - 10. Compute the following: A.) f(-2) + f(2)= B.) f(-2) f(2)=

Suppose f(x) = -x² - 4x - 10. Compute the following: A.) f(-2) + f(2)= B.) f(-2) f(2)=

Algebra and Trigonometry (6th Edition)
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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### Problem Statement Suppose \( f(x) = -x^2 - 4x - 10 \). Compute the following: #### A.) \[ f(-2) + f(2) = \] #### B.) \[ f(-2) - f(2) = \] ### Explanation 1. **Function Evaluation**: - To solve these problems, we need to evaluate the function \( f(x) \) at \( x = -2 \) and \( x = 2 \). 2. **Substitute and Simplify**: - For \( x = -2 \): \[ f(-2) = -(-2)^2 - 4(-2) - 10 \] Simplify inside the parentheses: \[ = -4 + 8 - 10 = -6 \] - For \( x = 2 \): \[ f(2) = -(2)^2 - 4(2) - 10 \] Simplify inside the parentheses: \[ = -4 - 8 - 10 = -22 \] 3. **Perform Operations**: - For \( f(-2) + f(2) \): \[ -6 + (-22) = -28 \] - For \( f(-2) - f(2) \): \[ -6 - (-22) = 16 \] ### Solution - **A.)** \( f(-2) + f(2) = -28 \) - **B.)** \( f(-2) - f(2) = 16 \) These steps should be clearly followed to achieve the correct results.
Transcribed Image Text:### Problem Statement Suppose \( f(x) = -x^2 - 4x - 10 \). Compute the following: #### A.) \[ f(-2) + f(2) = \] #### B.) \[ f(-2) - f(2) = \] ### Explanation 1. **Function Evaluation**: - To solve these problems, we need to evaluate the function \( f(x) \) at \( x = -2 \) and \( x = 2 \). 2. **Substitute and Simplify**: - For \( x = -2 \): \[ f(-2) = -(-2)^2 - 4(-2) - 10 \] Simplify inside the parentheses: \[ = -4 + 8 - 10 = -6 \] - For \( x = 2 \): \[ f(2) = -(2)^2 - 4(2) - 10 \] Simplify inside the parentheses: \[ = -4 - 8 - 10 = -22 \] 3. **Perform Operations**: - For \( f(-2) + f(2) \): \[ -6 + (-22) = -28 \] - For \( f(-2) - f(2) \): \[ -6 - (-22) = 16 \] ### Solution - **A.)** \( f(-2) + f(2) = -28 \) - **B.)** \( f(-2) - f(2) = 16 \) These steps should be clearly followed to achieve the correct results.
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