Q. 57 - Precalculus Enhanced with Graphing Utilities

Question

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

$f\left(x\right)=\frac{4}{\sqrt{x-9}}$

Step-by-Step Solution

Answer

The domain of the given function is $\left\{x\right|x\ge 9\}$

Step 1. Given Information

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

$f\left(x\right)=\frac{4}{\sqrt{x-9}}$

Step 2. The function f tells us to take 4 and divide this result by the square root of x - 9 .

This requires that 

$x-9\ge 0$

Add 9 on both side

$$\begin{gathered} x-9+9\ge 0+9 \\ x\ge 9 \end{gathered}$$ 

Step 3. The domain of f is

$\left\{x\right|x\ge 9\}$