Questions: f(x)=(25-x^2)/(sqrt(x+4))

To analyze the function \( f(x) = \frac{25-x^{2}}{\sqrt{x+4}} \), we can perform several tasks such as finding its domain, evaluating it at specific points, or plotting it. Here, I'll outline the approach to find the domain of the function:

1. Identify the constraints: The function has a square root in the denominator, which means the expression inside the square root must be non-negative, and the denominator must not be zero.
2. Solve the inequality: Solve \( x + 4 > 0 \) to ensure the square root is defined and non-zero.
3. Combine conditions: Use the results to determine the domain of \( f(x) \).

La función dada es \( f(x) = \frac{25 - x^2}{\sqrt{x + 4}} \). Para que la función esté definida, el denominador \(\sqrt{x + 4}\) debe ser mayor que cero. Esto implica que \(x + 4 > 0\).

Resolvemos la desigualdad \(x + 4 > 0\) para encontrar los valores de \(x\) que satisfacen esta condición: \[ x + 4 > 0 \implies x > -4 \]

El dominio de la función está determinado por los valores de \(x\) que satisfacen la desigualdad anterior. Por lo tanto, el dominio de \(f(x)\) es el intervalo \((-4, \infty)\).

El dominio de la función \( f(x) = \frac{25 - x^2}{\sqrt{x + 4}} \) es \(\boxed{(-4, \infty)}\).