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4. Find (f-g)(x) if f(x) = -2x + 4 and g(x)=x²-3x+5. O (f-g)(x) = -x²+x-1 O (f-g)(x)=x²-5x +9 O (f-g)(x) = -x²+x-5 O (f-g)(x) = x² +5x-9

4. Find (f-g)(x) if f(x) = -2x + 4 and g(x)=x²-3x+5. O (f-g)(x) = -x²+x-1 O (f-g)(x)=x²-5x +9 O (f-g)(x) = -x²+x-5 O (f-g)(x) = x² +5x-9

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 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.
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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