Question

In the following exercises, find the domain of each function.

$R\left(x\right)=\frac{8x^2-32x}{2x^2-6x-80}$

Short answer

The domain is$R-\left\{-5,8\right\}$

Step-by-step solution

Given Information

$R\left(x\right)=\frac{8x^2-32x}{2x^2-6x-80}$

Step 2. Factor the denominator  

Set the denominator zero

$$\begin{gathered} 2x^2-6x-80=0 \\ 2\left(x^2-3x-40\right)=0 \end{gathered}$$

$$\begin{gathered} x^2-3x-40=0 \\ \left(x-8\right)\left(x+5\right)=0 \end{gathered}$$

Step 3. Use the Zero Product Property  

$$\begin{gathered} \left(x-8\right)=0or\left(x+5\right)=0 \\ x=8,-5 \end{gathered}$$