Question

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

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

Short answer

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

Step-by-step solution

Step 1. Given Information

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

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

Step 2. The function G tells us to divide x+4 by x3-4x. 

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 functionGis$\left\{x\right|x\ne 0,x\ne -2,x\ne 2\}$