Question

find the domain of the function.
f(x)=\frac{4}{x - 12}+\frac{6}{x + 14}
the domain of f(x) is
(type your answer in interval notation.)

Explanation:

Step1: Identify values that make denominator zero

Set $x - 12=0$ and $x + 14=0$.
Solving $x - 12=0$ gives $x = 12$, and solving $x+14 = 0$ gives $x=-14$.

Step2: Determine domain

The domain of a rational - function excludes values that make the denominator zero. So the domain is all real numbers except $x = 12$ and $x=-14$. In interval notation, it is $(-\infty,-14)\cup(-14,12)\cup(12,\infty)$.

Answer:

$(-\infty,-14)\cup(-14,12)\cup(12,\infty)$