Question #123b8

Question

Question #123b8

1 Answer

Impact of this question

1617 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-12T01:12:28

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

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 $1$ ).

Science

Math

Humanities

... and beyond

Question #123b8

1 Answer

Explanation:

Related questions

Impact of this question