Question

In Problems 47– 62, find the domain of each function.

$g\left(x\right)=\frac{x}{x^2-16}$

Short answer

The domain of the given function is$\left\{x\right|x\ne -2,x\ne 2\}$

Step-by-step solution

Step 1. Given Information

In the given problems we have to find the domain of given function.

$g\left(x\right)=\frac{x}{x^2-16}$

Step 2. The function g tells us to divide x by x2-16.

Since division by $0$is not defined, the denominator $x^2-16$can never be $0$, so $x$can never equal $-4$or $4$. The domain of the function g is$\left\{x\right|x\ne -2,x\ne 2\}$