Q. 52 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The domain of the given function is $\left\{x\right|x\ne -4,x\ne 4\}$

Step 1. Given Information

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

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

Step 2. The function h tells us to divide 2 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 h is $\left\{x\right|x\ne -4,x\ne 4\}$.