Question

find the domain of the function.
$f(x) = \frac{24}{x^2 - 14x - 15}$
what is the domain of $f$?
( type your answer in interval notation. )

Explanation:

Step1: Set denominator equal to 0

$x^2 - 14x - 15 = 0$

Step2: Factor the quadratic equation

$(x - 15)(x + 1) = 0$

Step3: Solve for x-values

$x - 15 = 0 \implies x = 15$; $x + 1 = 0 \implies x = -1$

Step4: Define domain (exclude x=-1,15)

All real numbers except $x=-1$ and $x=15$, written as intervals.

Answer:

$(-\infty, -1) \cup (-1, 15) \cup (15, \infty)$