# What is the domain and range of # y=sqrt(x^2-1)#?

##### 1 Answer

Domain:

Range:

#### Explanation:

The domain of the function will be determined by the fact that the expression that's under the radical **must be positive** for real numbers.

Since

So, you need to have

#x^2 - 1 >=0#

#x^2 >=1#

Take the square root of both sides to get

#|x| >= 1#

This of course means that you have

#x >= 1" "# and#" "x<=-1#

The domain of the function will thus be

The range of the function will be determined by the fact that the square root of a real number **must always be positive**. The smallest value the function can take will happen for

#sqrt((-1)^2 -1) = 0" "# and#" "sqrt((1)^2 -1 ) = 0#

The range of the function will thus be

graph{sqrt(x^2-1) [-10, 10, -5, 5]}