Answer
The domain of g(x) is {${ x|x\ne4,x\ne-4}$}.
Work Step by Step
$g(x)=\frac{x}{x^2-16}$
To find the domain of a rational function, we must set the denominator equal to 0 and solve for x.
$x^2-16=0$
$x^2=16$
$x=\pm4$
This means that the domain is:
{${ x|x\ne4,x\ne-4}$}