Question

How do you find the Domain, I just want the steps

Answer 1

The domain is x

Answer 2

\[\frac{ \sqrt{x+3} }{ (x+8)(x+2) }\]

Answer 3

Of the x coordinate like (x, y)

Answer 4

Oh that domain.

Answer 5

NVM then.

Answer 6

lol okay, do you know how to find this domain?

Answer 7

There are some restrictions in the domain:

Hints:
Look in the numerator, it is \(\sqrt{x+3}\), this will be imaginary if the values of x is less than -3.

This rational function will be undefined if the value of the denominator is equal to zero. Thus, the zeros on the denominator were the restrictions in the domain.

Hope this helps!

Answer 8

@Data_LG2 I'm a bit confused now

Answer 9

which part are you confused with?

Answer 10

I'm just completely lost

Answer 11

okay let's do it step by step.

In the numerator, which values of x will make the value an imaginary number?

Answer 12

-3

Answer 13

not actually -3 because if you substitute x=-3 in the numerator it will be \(\sqrt{x+3}=\sqrt{-3+3}=\sqrt{0}=0\). If you will try x=-4 , you will get imaginary number. so you can say that \(x \ge-3, x \epsilon\ real\ numbers\)

Answer 14

did you get the first part?

Answer 15

Yeah a it, why would you use -4?

Answer 16

just an example to prove that any value of x below -3 will give an imaginary number.

Answer 17

Oh okay, so I'm trying to turn the numerator into a imaginary number?

Answer 18

yeah, to find the restrictions in the domain. But we are not done yet

Answer 19

Okay, I have to do something with denominator right?

Answer 20

yes, you have to find the zeros of the denominator.