Question

find the domain of the function.
g(x) = \frac{x}{x^{2}-16}
the domain of the function is
(type your answer in interval notation.)

Explanation:

Step1: Identify values that make denominator zero

Set the denominator $x^{2}-16 = 0$.

Step2: Solve the equation for x

Factor $x^{2}-16$ as $(x + 4)(x - 4)=0$. Then $x+4 = 0$ gives $x=-4$ and $x - 4=0$ gives $x = 4$.

Step3: Determine the domain

The domain of a rational function is all real - numbers except the values that make the denominator zero. So the domain is all real numbers except $x=-4$ and $x = 4$. In interval notation, it is $(-\infty,-4)\cup(-4,4)\cup(4,\infty)$.

Answer:

$(-\infty,-4)\cup(-4,4)\cup(4,\infty)$