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thewinterfawn
 2 years ago
Find the domain of the function.
thewinterfawn
 2 years ago
Find the domain of the function.

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thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=\sqrt[4]{x^2+3x}\]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Hint: Inside cannot be negative.

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0I don't understand how to start the problem. :/

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1\[f(x)=\sqrt[4]{g(x)}\] Solve the following inequality: \[g(x) \ge 0\] Solving this will give you your domain.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Because g can be zero and it can be positive, but it cannot be negative.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Like you know whatever g is. In this case your g is x^2+3x

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0Um. I'm not good at math so I'm having trouble understanding what you are saying. sorry.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Can you do fourth root of a negative number? Would that exist?

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0I don't think you can do that.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1like for real numbers anyways, no it wouldn't you are right that is why I'm allowing g to be positive or zero.

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0oh. so I just solve \[x^2+3x \ge0\]?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Np. Do you know how to solve it?

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0I think I do haha. Let me try it...

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0Um. Okay. I don't know how to. ):

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Ok. 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?

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0yeah it would be x=0, 3... i think.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Yep 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?

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry. The site was updating. ): The first and last intervals?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Yes 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.

thewinterfawn
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you! Your explanation was really helpful. (:
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