# What is the domain and range of #y=sqrt( x- (3x^2))#?

##### 1 Answer

Domain:

Range:

#### Explanation:

First, we'll find the range. (it's easier in this problem)

Since the square root radical is already present, we can say right out of the gate that the range is

Next, we'll find the domain.

Since you can't take the square root of a negative number, (over the set of real numbers) we'll see what values of

Just to make it prettier, we'll multiply both sides by negative 1. It makes the coefficient of the squared term positive. Because we are multiplying by a negative, we'll also have to flip the inequality.

We factor out an

However, now we have to use critical number analysis. We'll test various values of

To find critical numbers, we just use the values of

Since we want the number to be less than or equal to zero, we want only one of the two multiplied things (

To start, we'll test a value of

When

Next, we'll try a value of

Lastly, we have to try a value greater than both critical numbers,

That means that our output will be positive, and therefore greater than zero. It does not work as a solution.