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Domain of a function - f(x,y)=root(1-x)+root(1-y)

  1. Sep 22, 2012 #1

    FOIWATER

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    I have came up with a solution for this - in order for this function to be defined, we must have an x and y between negative infinity up to and including the number 1.

    If asked to graph this domain, does the domain lie on the x-y plane of three dimensional space, and is it the intersection of the domains of x and y?

    I know the only sensible way to my question will likely go over my head - I Just started vector calculus - so no worries, I find it difficult for this to make sense to me.

    I am thinking of the domain as the values "under" the z-plane in 3d space, if that makes any sense... at all - or above! or maybe a point in three-d space is ON the plane, when z is zero?
     
    Last edited: Sep 22, 2012
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  3. Sep 22, 2012 #2

    jedishrfu

    Staff: Mentor

    i think this is simplay a 2D problem in x and y unless you want to make it 3D by stating f(x,y)=z

    next what does the root(1-x) mean? I don't understand how to even plot this if I could.
     
  4. Sep 22, 2012 #3

    FOIWATER

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    well it's 1-x all under a square root sign

    root(1-x) = sqrt(1-x)

    you know?
     
  5. Sep 22, 2012 #4

    jedishrfu

    Staff: Mentor

    okay got it so thats why x>1 or y>1 is out of bounds if you're dealing with real numbers but okay for complex numbers.

    so I got a sideways parabola from ending at z=0 x=1 y=1

    You might google on graph 3D calculator and try your formula. I did but I didnt have the flash plugin installed (I'm on linux) so I had to imagine how it looks rotating the x curve around (1,1,0)
     
  6. Sep 23, 2012 #5

    FOIWATER

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    really..hmm.. I got a rectangular plane - I don't think we are considering z here? hold it constant, and just focus on y and x right?

    so we have x and y have both to be less than or equal to negative one. So they intersect on a rectangular plane going back to negative infinity....?
     
  7. Sep 23, 2012 #6
    Assuming you are just dealing in real numbers, your domain is simply to do with x and y and it is [itex]\{x,y \in\mathbb R: x \leq 1,\ y \leq 1\}[/itex]
     
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