Question

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

$p\left(x\right)=\sqrt{\frac{2}{x-1}}$

Short answer

The domain of the given function is$\left\{x\right|x\ge 1\}$

Step-by-step solution

Step 1. Given Information 

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

$p\left(x\right)=\sqrt{\frac{2}{x-1}}$

Step 2. The function p tells us to take the square root of 2 and divide this result by the square root of x-1.

This requires that

$x-1\ge 0$

Add 1 on both side

$$\begin{gathered} x-1+1\ge 0+1 \\ x\ge 1 \end{gathered}$$

Step 3. The domain of p is

$\left\{x\right|x\ge 1\}$