Domain of a Rational Function III

Problem 267: State the domain of the function

$f(x) = \frac{9x - 2}{x^2 - x - 72}$

in interval notation!

Solution: Finding the domain of a rational expression required us to find the value of $x$ that would make the denominator zero. Thus

$x^2 - x - 72 = ( x-9)(x + 8) \implies x - 9 = 0 \ \text{or} \ x + 8 = 0 \implies x = 9 \ \text{or} \ x = -8.$

This means that our rational function is defined for all values of $x$ except for $x = 9$ or $x = -8. Therefore, the domain is

$(-\infty, -8) \cup (-8, 9) \cup (9, \infty).$