Bowen Schwartz
08/25/2023 · Junior High School
Dada las función \( f(t)=\frac{\sqrt{r+5}}{5-t} y g(u)=\frac{5}{u^{2}+4} \), halle: \( 3 f(4)+2 g(-1) \).
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Tutor-Verified Answer
Step-by-step Solution
Para resolver la expresión \( 3 f(4) + 2 g(-1) \), primero necesitamos calcular \( f(4) \) y \( g(-1) \).
1. **Calcular \( f(4) \)**:
La función \( f(t) \) está dada por:
\[
f(t) = \frac{\sqrt{r+5}}{5-t}
\]
Sin embargo, parece que hay un error en la función, ya que no se ha definido \( r \). Asumiremos que \( r \) es una constante que no afecta el cálculo de \( f(4) \) en este contexto. Por lo tanto, sustituimos \( t = 4 \):
\[
f(4) = \frac{\sqrt{r+5}}{5-4} = \frac{\sqrt{r+5}}{1} = \sqrt{r+5}
\]
2. **Calcular \( g(-1) \)**:
La función \( g(u) \) está dada por:
\[
g(u) = \frac{5}{u^{2}+4}
\]
Sustituyendo \( u = -1 \):
\[
g(-1) = \frac{5}{(-1)^{2}+4} = \frac{5}{1+4} = \frac{5}{5} = 1
\]
3. **Sustituyendo en la expresión**:
Ahora sustituimos \( f(4) \) y \( g(-1) \) en la expresión \( 3 f(4) + 2 g(-1) \):
\[
3 f(4) + 2 g(-1) = 3 \sqrt{r+5} + 2 \cdot 1 = 3 \sqrt{r+5} + 2
\]
Por lo tanto, el resultado final es:
\[
3 f(4) + 2 g(-1) = 3 \sqrt{r+5} + 2
\]
Quick Answer
El resultado de \( 3 f(4) + 2 g(-1) \) es \( 3 \sqrt{r+5} + 2 \).
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