Pregunta
The function \( f \) is defined as follows. \[ f(x)=\frac{x^{2}+4 x-21}{x^{2}-4} \] Find \( f(-5) \). Simplify your answer as much as possible. If applicable, click on
Ask by Wade Nguyen. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( f(-5) = -\frac{16}{21} \)
Solución
1. Substitute \( x = -5 \) into \( f(x) \):
\[
f(-5)=\frac{(-5)^2+4(-5)-21}{(-5)^2-4}
\]
2. Compute the numerator:
\[
(-5)^2+4(-5)-21 = 25-20-21 = -16
\]
3. Compute the denominator:
\[
(-5)^2-4 = 25-4 = 21
\]
4. Therefore, the value is:
\[
f(-5)=\frac{-16}{21}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To find \( f(-5) \), we need to substitute \(-5\) into the function: \[ f(-5) = \frac{(-5)^{2} + 4(-5) - 21}{(-5)^{2} - 4} \] Calculating the numerator: \[ (-5)^{2} = 25, \quad 4(-5) = -20 \] \[ (-5)^{2} + 4(-5) - 21 = 25 - 20 - 21 = 25 - 41 = -16 \] Now calculating the denominator: \[ (-5)^{2} - 4 = 25 - 4 = 21 \] Putting it all together, we have: \[ f(-5) = \frac{-16}{21} \] Thus, the simplified answer is: \[ \boxed{-\frac{16}{21}} \]
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