Question

Find the domain of each function.

$g\left(x\right)=\frac{x}{\sqrt{x+8}}$

Short answer

The domain of the function$g\left(x\right)=\frac{x}{\sqrt{x+8}}$ is $\left\{x\right|x>-8\}$.

Step-by-step solution

Step 1. Given information 

We have been given a function $g\left(x\right)=\frac{x}{\sqrt{x+8}}$.

We have to find its domain.

Step 2. Find the values that make the function defined 

Square root function is defined for nonnegative numbers and also the numerator should not be zero.

Therefore $x+8$should be positive.

$$\begin{gathered} x+8>0 \\ x+8-8>0-8(\mathrm{Subtract}8\mathrm{from}\mathrm{both}\mathrm{sides}) \\ x>-8 \end{gathered}$$

Therefore, the domain will be $\left\{x\right|x>-8\}$.