Q. 51 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

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 x 2 - 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 $\left\{x\right|x\ne -2,x\ne 2\}$