Question

Find the domain of the function.

Answer 1

\[f(x)=\sqrt[4]{x^2+3x}\]

Answer 2

Hint: Inside cannot be negative.

Answer 3

I don't understand how to start the problem. :/

Answer 4

\[f(x)=\sqrt[4]{g(x)}\]
Solve the following inequality:
\[g(x) \ge 0\]
Solving this will give you your domain.

Answer 5

Because g can be zero and it can be positive, but it cannot be negative.

Answer 6

Like you know whatever g is. In this case your g is x^2+3x

Answer 7

Um. I'm not good at math so I'm having trouble understanding what you are saying. sorry.

Answer 8

Can you do fourth root of a negative number?
Would that exist?

Answer 9

I don't think you can do that.

Answer 10

like for real numbers anyways, no it wouldn't
you are right
that is why I'm allowing g to be positive or zero.

Answer 11

oh. so I just solve \[x^2+3x \ge0\]?

Answer 12

That is right.

Answer 13

thank you. :D

Answer 14

Np. Do you know how to solve it?

Answer 15

I think I do haha. Let me try it...

Answer 16

Um. Okay. I don't know how to. ):

Answer 17

Ok. Just think domain are the x values where the function can exist for.
If you talk about range later, just ask yourself what are the y values where the function exist.
---


Ok...
So do you know how to solve x^2+3x=0?

Answer 18

yeah it would be x=0, -3... i think.

Answer 19

Yep yep...You did x(x+3)=0 which implies x=0 or x+3=0
great job...

Now make a number line (on this number line you would include the zeros, -3 or 0 , but you would also include what x values made the expression not existing which we don't have any for x^2+3x)

so here we go

---------------|-------------|-----------
-3 0

Test all 3 intervals.

You are looking for what intervals make x^2+3x positive since we are trying to solve x^2+3x>0

(We already solved when x^2+3x=0 )
(-4)^2+3(-4) (-1)^2+3(-1) (1)^2+3(1)
= = =
---------------|-------------|-----------
-3 0

Now all I'm doing is plugging in numbers around my zeros (-3 and 0)
This is to test the intervals
Remember we are looking for positive output
Which one of those expressions I wrote above those intervals gives us positive output?

Answer 20

Sorry. The site was updating. ):
The first and last intervals?

Answer 21

Yes so the domain is the first and last intervals include x=-3, 0.

So you would state it as (-inf, -3] U [0, inf)

We don't want to include anything in between -3 and 0 because like you said that gave us negative output.

And yeah sorry os went down earlier.

Answer 22

Thank you! Your explanation was really helpful. (: