Q. 54 - Precalculus Enhanced with Graphing Utilities

Question

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

$G\left(x\right)=\frac{x+4}{x^3-4x}$

Step-by-Step Solution

Answer

The domain of the given function is $\left\{x\right|x\ne 0,x\ne -2,x\ne 2\}$

Step 1. Given Information

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

$G\left(x\right)=\frac{x+4}{x^3-4x}$

Step 2. The function G tells us to divide x + 4 by x 3 - 4 x .

Since division by $0$ is not defined, the denominator $x^3-4x$ can never be $0$, so $x$ can never equal $0,-2$ or $2$. The domain of the function G is $\left\{x\right|x\ne 0,x\ne -2,x\ne 2\}$