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

myininayaBest ResponseYou've already chosen the best response.1
Hint: Inside cannot be negative.
 6 months ago

thewinterfawnBest ResponseYou've already chosen the best response.0
I don't understand how to start the problem. :/
 6 months ago

myininayaBest 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.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Because g can be zero and it can be positive, but it cannot be negative.
 6 months ago

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

thewinterfawnBest ResponseYou've already chosen the best response.0
Um. I'm not good at math so I'm having trouble understanding what you are saying. sorry.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Can you do fourth root of a negative number? Would that exist?
 6 months ago

thewinterfawnBest ResponseYou've already chosen the best response.0
I don't think you can do that.
 6 months ago

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

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

myininayaBest ResponseYou've already chosen the best response.1
Np. Do you know how to solve it?
 6 months ago

thewinterfawnBest ResponseYou've already chosen the best response.0
I think I do haha. Let me try it...
 6 months ago

thewinterfawnBest ResponseYou've already chosen the best response.0
Um. Okay. I don't know how to. ):
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
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?
 6 months ago

thewinterfawnBest ResponseYou've already chosen the best response.0
yeah it would be x=0, 3... i think.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
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?
 6 months ago

thewinterfawnBest ResponseYou've already chosen the best response.0
Sorry. The site was updating. ): The first and last intervals?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
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.
 6 months ago

thewinterfawnBest ResponseYou've already chosen the best response.0
Thank you! Your explanation was really helpful. (:
 6 months ago
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