# Question 123b8

Aug 12, 2017

$\left\{x \in \mathbb{R} : - 6 \le x \le 1\right\}$

#### 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 $0$ when $x = - 6$ and $x = 1$, so what we need to do is figure out if the domain is real in between these two numbers or outside of these values.

Plugging in a value between $- 1$ and $6$ (let's say $0$):

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

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

$- 6 \le x \le 1$

Plugging in $- 7$ and $2$ yields

$- \left(- 7 + 6\right) \left(- 7 - 1\right) = - 8$

$- \left(2 + 6\right) \left(2 - 1\right) = - 8$

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 $x$ is greater than or equal to $- 6$ and less than or equal to $1$).