Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of each function. 

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

Step-by-Step Solution

Answer

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

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 $\left\{x\right|x>-8\}$.