Pregunta
For the functions \( f(x)=2 x^{2}-3 x-8 \), and \( g(x)=x-3 \), find (f \( -g)(x) \) a) \( 2 x^{2}-2 x-5 \) b) \( 2 x^{2}-4 x-11 \) c) \( x^{2}-2 x-11 \) d) \( 2 x^{2}-4 x-5 \) e) \( 2 x^{2}-2 x-11 \)
Ask by Hall Garrett. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\((f - g)(x) = 2x^2 - 4x - 5\), so the answer is d) \(2x^2 - 4x - 5\).
Solución
We start by finding the function \((f - g)(x)\):
1. Write the function definitions:
- \( f(x)=2x^2-3x-8 \)
- \( g(x)=x-3 \)
2. Subtract \( g(x) \) from \( f(x) \):
\[
(f-g)(x) = f(x)-g(x) = \left(2x^2-3x-8\right) - \left(x-3\right)
\]
3. Distribute the negative sign:
\[
(f-g)(x) = 2x^2-3x-8 - x + 3
\]
4. Combine like terms:
- Combine the \(x\)-terms: \(-3x - x = -4x\)
- Combine the constants: \(-8 + 3 = -5\)
Thus,
\[
(f-g)(x) = 2x^2 - 4x - 5
\]
The correct answer is:
d) \( 2x^2-4x-5 \)
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Extra Insights
To find \( (f - g)(x) \), we need to subtract the function \( g(x) \) from \( f(x) \): 1. Start with the functions: - \( f(x) = 2x^2 - 3x - 8 \) - \( g(x) = x - 3 \) 2. Find \( f(x) - g(x) \): \[ (f - g)(x) = f(x) - g(x) = (2x^2 - 3x - 8) - (x - 3) \] 3. Distributing the negative sign: \[ f(x) - g(x) = 2x^2 - 3x - 8 - x + 3 \] 4. Combine like terms: - Combine \( -3x \) and \( -x \): \[ -3x - x = -4x \] - Combine \( -8 \) and \( +3 \): \[ -8 + 3 = -5 \] 5. All together: \[ (f - g)(x) = 2x^2 - 4x - 5 \] So the final answer is \( (f - g)(x) = 2x^2 - 4x - 5 \), which corresponds to option **d)**.
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