Domain of a Rational Function II

Problem 265: State the domain of the function

$f(x) = \frac{8x + 7}{9x - 8}$

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

$9x - 8 = 0 \implies 9x = 8 \implies x = \frac{8}{9}.$

This means that our rational function is defined for all values of $x$ except for $x = \frac{8}{9}$ . Therefore, the domain is

$\left(-\infty,\frac{8}{9} \right) \cup \left(\frac{8}{9}, \infty \right).$