Pregunta
Question Given the definitions of \( f(x) \) and \( g(x) \) below, find the value of \( g(f(-5)) \) \[ \begin{array}{l}f(x)=x^{2}+x-12 \\ g(x)=-2 x-15\end{array} \]
Ask by French Pollard. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( g(f(-5)) = -31 \)
Solución
1. Substitute \(-5\) into \( f(x) \):
\[
f(-5) = (-5)^2 + (-5) - 12 = 25 - 5 - 12 = 8
\]
2. Now substitute \( f(-5) = 8 \) into \( g(x) \):
\[
g(8) = -2 \times 8 - 15 = -16 - 15 = -31
\]
The value of \( g(f(-5)) \) is \(-31\).
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Simplifique esta solución Bonus Knowledge
To find the value of \( g(f(-5)) \), we first need to compute \( f(-5) \). Using the definition of \( f(x) \): \[ f(-5) = (-5)^2 + (-5) - 12 \] Calculating step-by-step: \[ f(-5) = 25 - 5 - 12 = 25 - 17 = 8 \] Now we have \( f(-5) = 8 \). Next, we compute \( g(8) \) using the definition of \( g(x) \): \[ g(8) = -2(8) - 15 \] Calculating it out: \[ g(8) = -16 - 15 = -31 \] Thus, the value of \( g(f(-5)) \) is \(-31\).
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