Question

rational expressions
evaluating a rational function: problem type 2
the function f is defined as follows.
$f(x) = \frac{x^2 + 5x + 6}{x^2 - 25}$
find $f(-5)$.
simplify your answer as much as possible. if applicable, click on \undefined\.
$f(-5) = \boxed{}$
(options: fraction, mixed number, undefined)

Explanation:

Step1: Analyze the denominator at \( x = -5 \)

To find \( f(-5) \), we first check the denominator of the rational function \( f(x)=\frac{x^{2}+5x + 6}{x^{2}-25} \) when \( x=-5 \). Substitute \( x = -5 \) into the denominator: \( (-5)^{2}-25=25 - 25=0 \).

Step2: Determine the function's status

A rational function is undefined when its denominator is zero (since division by zero is undefined in mathematics). Since the denominator is zero when \( x=-5 \), the function \( f(x) \) is undefined at \( x = -5 \).

Answer:

Undefined