Question

find the domain of the function.
$f(x) = \frac{x + 3}{6 - x}$

Explanation:

Step1: Identify undefined condition

A rational function is undefined when its denominator equals 0. Set the denominator equal to 0:
$6 - x = 0$

Step2: Solve for excluded x-value

Solve the equation to find the value that makes the function undefined:
$x = 6$

Step3: Define valid x-values

The function is defined for all real numbers except the excluded value.

Answer:

All real numbers except $x=6$, or in interval notation: $(-\infty, 6) \cup (6, \infty)$