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,...
Related questions
Question
![**Problem 4:**
Find \((f - g)(x)\) if \(f(x) = -2x + 4\) and \(g(x) = x^2 - 3x + 5\).
Select the correct option:
- \( \circ \) \((f - g)(x) = -x^2 + x - 1\)
- \( \circ \) \((f - g)(x) = x^2 - 5x + 9\)
- \( \circ \) \((f - g)(x) = -x^2 + x - 5\)
- \( \circ \) \((f - g)(x) = x^2 + 5x - 9\)
---
**Explanation:**
To solve the problem, subtract the function \(g(x)\) from \(f(x)\):
\[
(f - g)(x) = f(x) - g(x) = (-2x + 4) - (x^2 - 3x + 5)
\]
Simplify the expression by distributing the negative sign and combining like terms:
\[
= -2x + 4 - x^2 + 3x - 5
\]
\[
= -x^2 + (-2x + 3x) + (4 - 5)
\]
\[
= -x^2 + x - 1
\]
The correct answer is \((-x^2 + x - 1\)), corresponding to the first option.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc131e709-cc3e-4f0d-91ec-97e8c645b93d%2F1bf96297-2a3d-40d3-8944-0b36e9e9fc52%2Fb9vqevi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4:**
Find \((f - g)(x)\) if \(f(x) = -2x + 4\) and \(g(x) = x^2 - 3x + 5\).
Select the correct option:
- \( \circ \) \((f - g)(x) = -x^2 + x - 1\)
- \( \circ \) \((f - g)(x) = x^2 - 5x + 9\)
- \( \circ \) \((f - g)(x) = -x^2 + x - 5\)
- \( \circ \) \((f - g)(x) = x^2 + 5x - 9\)
---
**Explanation:**
To solve the problem, subtract the function \(g(x)\) from \(f(x)\):
\[
(f - g)(x) = f(x) - g(x) = (-2x + 4) - (x^2 - 3x + 5)
\]
Simplify the expression by distributing the negative sign and combining like terms:
\[
= -2x + 4 - x^2 + 3x - 5
\]
\[
= -x^2 + (-2x + 3x) + (4 - 5)
\]
\[
= -x^2 + x - 1
\]
The correct answer is \((-x^2 + x - 1\)), corresponding to the first option.
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