Question

question 10 of 10, step 1 of 1
determine the implied domain of the following function. express your answer in interval notation.
$f(x) = \frac{12}{x - 13}$
answer

Explanation:

Step1: Identify undefined input

A rational function is undefined when its denominator equals 0. Set the denominator equal to 0:
$x - 13 = 0$

Step2: Solve for excluded x-value

Solve the equation to find the restricted value:
$x = 13$

Step3: Write domain in interval notation

The function is defined for all real numbers except $x=13$. Split the real number line into two intervals:
$(-\infty, 13) \cup (13, \infty)$

Answer:

$(-\infty, 13) \cup (13, \infty)$