thewinterfawn 2 years ago Find the domain of the function.

1. thewinterfawn

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

2. myininaya

Hint: Inside cannot be negative.

3. thewinterfawn

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

4. myininaya

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

5. myininaya

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

6. myininaya

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

7. thewinterfawn

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

8. myininaya

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

9. thewinterfawn

I don't think you can do that.

10. myininaya

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

11. thewinterfawn

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

12. myininaya

That is right.

13. thewinterfawn

thank you. :D

14. myininaya

Np. Do you know how to solve it?

15. thewinterfawn

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

16. thewinterfawn

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

17. myininaya

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?

18. thewinterfawn

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

19. myininaya

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?

20. thewinterfawn

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

21. myininaya

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.

22. thewinterfawn