# Question #123b8

##### 1 Answer

#### Explanation:

In the realm of **real numbers**, the radicand must be positive (the square root of *negative* numbers is a nonreal quantity).

We can factor the radicand into

#ul(sqrt(-(x+6)(x-1))#

We see that the function equals *in between* these two numbers or *outside* of these values.

Plugging in a value between

#-(0+6)(0-1) = color(red)(6#

Since it is **positive**, we know the domain is at least

#-6<= x <= 1#

Plugging in

#-(-7+6)(-7-1) = -8#

#-(2+6)(2-1) = -8#

Since these are both *negative*, our final domain is

#color(blue)(ulbar(|stackrel(" ")(" "{x in RR: -6<= x <= 1}" ")|)#

(The domain is all real numbers such that