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

##### 1 Answer

Domain:

Range:

#### Explanation:

The domain of the function will be determined by the expression that's under the square root.

More specifically, for *real numbers*, the square root is defined exclusively for **positive numbers**, which means that

This quadratic has two solutions

For numbers **outside** the **Inside** the interval, this expression will be negative, which means that the domain of the function cannot include values in the

The domain of the function will thus be

The range of the function will be determine by the fact that the square root will always give a **positive value** for real numbers.

This means that the range of the will be

graph{sqrt(x^2-1) [-7.9, 7.904, -3.946, 3.956]}