Question

algebra
review passage
express the domain of the function using interval notation.
question
$g(x) = \frac{x - 6}{x + 2}$
select a single answer
$(-\infty, 6) \cup (6, \infty)$
$(-\infty, \infty)$
$(-\infty, -2) \cup (-2, \infty)$
$(-\infty, -6) \cup (-6, \infty)$
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Explanation:

Step1: Identify undefined point

A rational function is undefined when its denominator equals 0. Set $x+2=0$.

Step2: Solve for x

$x+2=0 \implies x=-2$

Step3: Write domain in intervals

The function is defined for all real numbers except $x=-2$, so the domain is $(-\infty,-2)\cup(-2,\infty)$.

Answer:

$(-\infty,-2)\cup(-2,\infty)$