Question

Question #123b8

Answer 1

`{x in RR: -6<= x <= 1}`

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<= x <= 1`

Plugging in `-7` and `2` yields

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