Pregunta
Let \( f(x)=x^{2}-x+8 \) and \( g(x)=2 x-6 \). Find \( g(9) \) and \( f(g(9)) \). \( g(9)=\square \) (Simplify your answer.)
Ask by Burgess Wagner. in the United States
Feb 24,2025
Solución de inteligencia artificial de Upstudy
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g(9) = 12 and f(g(9)) = 140.
Solución
To solve the problem, we need to compute two values step by step.
1. First, find g(9):
g(x) = 2x - 6, so
g(9) = 2(9) - 6 = 18 - 6 = 12.
2. Next, compute f(g(9)) which is f(12):
f(x) = x² - x + 8, so
f(12) = (12)² - 12 + 8 = 144 - 12 + 8 = 140.
Thus, the answer is:
g(9) = 12 and f(g(9)) = 140.
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Simplifique esta solución Bonus Knowledge
To find \( g(9) \), we will substitute \( x = 9 \) into the function \( g(x) \). \[ g(9) = 2(9) - 6 = 18 - 6 = 12. \] Now, we need to find \( f(g(9)) \), which means we will substitute \( g(9) = 12 \) into \( f(x) \): \[ f(12) = 12^2 - 12 + 8. \] Calculating this step by step: \[ 12^2 = 144, \] \[ 144 - 12 = 132, \] \[ 132 + 8 = 140. \] Thus, \( f(g(9)) = f(12) = 140 \). So the final answers are: \[ g(9) = 12 \quad \text{and} \quad f(g(9)) = 140. \]
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