# How do you find the domain and range of #1 / root4 (x^2 -5x)#?

##### 1 Answer

Domain:

Range:

#### Explanation:

**Finding the Domain**

To find the domain we want to look at where the function goes undefined. The first thing that might spring to mind is if the denominator equals zero. To find when that happens, we can solve this equation:

By the zero factor principle we get that the solutions are

The other possibility that might make the function undefined is if the bit inside the 4th root is negative. To find when this occurs, we solve this inequality:

To find the negative possibilities for this inequality, we need to look at the intervals between the zeroes since that is where the function could potentially go negative. For the function to be negative, only one of the products may be negative.

On the interval

On the interval

And finally

This means that the function is undefined on the interval

**Finding the Range**

The vertical asymptotes caused by the zeroes in the denominator would normally go to

This means that our will be all the positive real numbers,