Q. 58 - Precalculus Enhanced with Graphing Utilities

Question

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

$f\left(x\right)=\frac{x}{\sqrt{x-4}}$

Step-by-Step Solution

Answer

The domain of the given function is $\left\{x\right|x\ge 4\}$

Step 1. Given Information

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

$f\left(x\right)=\frac{x}{\sqrt{x-4}}$

Step 2. The function f tells us to take x and divide this result by the square root of x - 4

This requires that

$x-4\ge 0$

Add 4 on both side

$$\begin{gathered} x-4+4\ge 0+4 \\ x\ge 4 \end{gathered}$$

Step 3. The domain of f is

$\left\{x\right|x\ge 4\}$