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

##### 1 Answer

Domain:

#### Explanation:

Right from the start, you know that the domain of the function must only include values of **positive**.

In other words, you need to exclude from the function's domain any value of

#x - 3x^2 < 0#

The expression under the square root can be factored to give

#x - 3x^2 = x * (1 - 3x)#

Make this expression equal to zero to find the values of *negative*.

#x * (1 - 3x) = 0 implies {(x = 0), (x = 1/3) :}#

So, in order for this expression to be *positive*, you need to have

**or**

Now, for

#{(x<0), (1 - 3x > 0) :} implies x * (1-3x) < 0#

Likewise, for

#{(x > 0), (1 - 3x > 0) :} implies x * (1-3x) < 0#

This means that the only values of *positive* can be found in the interval

Any other value of

graph{sqrt(x-3x^2) [-0.466, 0.866, -0.289, 0.377]}