# How do you find the domain and range of #f(x) =sqrt( x - 1) - 1/sqrt( 2-x)#?

##### 1 Answer

#### Answer:

#### Explanation:

We have

Whenever we have a function with a square root, we know that the square root has to be bigger than or equal to

For the second square root, we need to be more careful, because we have

So our domain is

To find the range, we need to find the stationary point and find if the function is increasing or decreasing.

Since

Let

Solving for

Therefore,