Question

Can someone help?

Answer 1

I need to find the domain in interval notation

Answer 2

Hint:

Since you can't take the square root of a negative number, this means that

x(x-15) >= 0

Answer 3

would I distribute that x?

Answer 4

x^2-15>=0
x^2>=15

Answer 5

you can, but think about it like this

when is x(x-15) positive?

We have 4 cases

case 1) if x is positive and x-15 is positive, then x(x-15) is positive

case 2) if x is negative and x-15 is positive, then x(x-15) is negative

case 3) if x is positive and x-15 is negative, then x(x-15) is negative

case 4) if x is negative and x-15 is negative, then x(x-15) is positive

Answer 6

So you can see that x(x-15) is positive in case 1) and case 4)

Answer 7

woah, that confused me...

Answer 8

which part is throwing you off?

Answer 9

Think of x and x-15 as factors of some number

Answer 10

case 1) positive times positive = positive

case 2) negative times positive = negative

case 3) positive times negative = negative

case 4) negative times negative = positive

Answer 11

Does that make (a bit more) sense?

Answer 12

yeah, just simple multiplication rules lol

Answer 13

that's ok, I was confusing it a little bit

Answer 14

To answer the original question, you have to find the interval where

x is positive and x-15 is positive

OR

x is negative and x-15 is negative

Optionally, you can graph x(x-15) or x^2 - 15 and see which portions of the graph are above the x-axis