Domain of Rational Functions

Problem 265: State the domain of the function

$f(x) = \frac{9x + 1}{9x}$

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

$9x = 0 \implies x = 0.$

This means that our rational function is defined for all values of $x$ except for $x = 0$ . Therefore, the domain is

$(-\infty, 0) \cup (0, \infty).$