anonymous
  • anonymous
Find the domain of the function. g(x)=^4sq.rt x^2+2x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
yep that's what it's supposed to be
IrishBoy123
  • IrishBoy123
scan or link the question pls
IrishBoy123
  • IrishBoy123
sorry, been here done that! just scan or link it :p

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anonymous
  • anonymous
the one you typed is the correct one
IrishBoy123
  • IrishBoy123
scan or link your question no point is answering to ghosts
anonymous
  • anonymous
i don't know how to scan it and the link wont work since it's under my account name.. you already know what the problem looks like, you sent it yourself, so it should be good enough?
anonymous
  • anonymous
\[\sqrt[4]{x^2+2x}\]
anonymous
  • anonymous
?
freckles
  • freckles
what happens if you have this\[\sqrt[4]{-1}\]? does this exist over the real numbers?
anonymous
  • anonymous
I don't think so since you shouldnt have -'s under a radical
freckles
  • freckles
great so you want x^2+2x to be positive or zero right?
anonymous
  • anonymous
yeah
freckles
  • freckles
for a number to be positive or equal it must be greater than or equal to 0
freckles
  • freckles
so you basically need to solve x^2+2x>=0
freckles
  • freckles
to find the domain
anonymous
  • anonymous
do we just get rid of the radical then?
freckles
  • freckles
you told me just a sec ago that we didn't want the thing under the radical to be negative which means we want it to be zero or positive
freckles
  • freckles
the thing under the radical was x^2+2x
freckles
  • freckles
so you want x^2+2x>=0
anonymous
  • anonymous
it has to be in interval notation
anonymous
  • anonymous
so would I start with (0,_)
freckles
  • freckles
you would solve x^2+2x>=0
freckles
  • freckles
then we can put an interval notation
anonymous
  • anonymous
x^2>or= -2x
anonymous
  • anonymous
and then would we square both sides?? because then there'd be a negative on the right
freckles
  • freckles
\[x^2+2x \ge 0 \\ x(x+2) \ge 0\] draw a number line x(x+2) is zero when x=0 or x+2=0 |dw:1441829182423:dw| test the intervals
freckles
  • freckles
|dw:1441829210139:dw|
anonymous
  • anonymous
OHH so x can equal 0 or -2?
anonymous
  • anonymous
can;t*
freckles
  • freckles
let me know when you have tested the intervals and yes x=-2 and x=0 will be included in the solution for the domain but we have to also consider the numbers around them
anonymous
  • anonymous
3,-1, and 3?
freckles
  • freckles
|dw:1441829448997:dw|
freckles
  • freckles
so this tells us x^2+2x is positive on the first and last intervals
freckles
  • freckles
in this number line
freckles
  • freckles
|dw:1441829505021:dw|
anonymous
  • anonymous
(-infinity,-2)U(-2,0)U(-2,0)U(0,infinity)?
freckles
  • freckles
you need to include both -2 and 0... also why are you include (-2,0) x^2+2x is negative on (-2,0)
freckles
  • freckles
remember we were trying to find x such that x^2+2x was positive or zero
freckles
  • freckles
we found x^2+2x was zero at x=-2, x=0 we found x^2+2x was positive for values to the left of -2, also values to right of 0
freckles
  • freckles
you should not include (-2,0) do you understand why? you should include -2 and 0 in your solution do you understand this also?
anonymous
  • anonymous
no I don't :-(
freckles
  • freckles
hmm... so do you remember when we tested the intervals earlier and for the member that represented the set of numbers on (-2,0) we got a negative number?
freckles
  • freckles
|dw:1441829916519:dw|
freckles
  • freckles
|dw:1441829938691:dw| I put check marks on the intervals we want because we were looking for intervals where x^2+2x was positive I put an X mark on intervals we don't want because we were not looking for when x^2+2x was negative.
freckles
  • freckles
the 4 root of 0 exists and it is 0 so x^2+2x=0 will satisfy our domain x(x+2)=0 when x=0 and x=-2 these numbers have to be a part of the domain
freckles
  • freckles
|dw:1441830041033:dw|
anonymous
  • anonymous
oh, so we dont include -2,0 because it would result in a negative
freckles
  • freckles
no we don't include (-2,0) because any number from that set would result in a negative we do include -2 and 0 though because pluggin in those numbers result in zero
anonymous
  • anonymous
okay so we include those but not (-2,0)
freckles
  • freckles
yes any number from (-2,0) when pluggin in to x^2+2x will give you a negative number you have already said the 4th root of a negative number doesn't exist over the real numbers
anonymous
  • anonymous
so how would I write that in interval notationn without including (-2,0)

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