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Homework Help: How to find the domain in one dimension

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data
    I am trying to find the domain of the following..

    R^2 to R^3 of g(x,y) = (x-y,x+y,3*x)
    R^3 to R of h(x,y,z) = x/(y+z)

    2. Relevant equations



    3. The attempt at a solution

    I don't know how to start. I know how to find the domain in one dimension but how do you do it in 2 or 3 dimensions???
    Thanks
     
    Last edited: Jan 21, 2010
  2. jcsd
  3. Jan 21, 2010 #2

    Dick

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    Science Advisor
    Homework Helper

    Re: Domain

    Your second function is actually R^3->R. Since they didn't tell you what the domain is, you just want to pick the domain of f:A->B to be all of the points in A where the function is defined.
     
  4. Jan 21, 2010 #3
    Re: Domain

    so for the first one can just do from (-infinity to infinity) ????

    can i just put in any value of x i want to?
     
  5. Jan 21, 2010 #4

    Mark44

    Staff: Mentor

    Re: Domain

    For the first one, your domain is not just R, the real line; it's the real plane, R2. For the second one, there is a restriction on y and z.
     
  6. Jan 21, 2010 #5

    Dick

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    Re: Domain

    Basically, yes. But the domain isn't (-infinity,infinity), that's a subset of R. The domain should be a subset of R^2. How about saying it's ALL of R^2?
     
  7. Jan 21, 2010 #6
    Re: Domain

    So the first one domain = R^2 the real plane

    second one = is y+z not equal to '0'

    is that right?
     
  8. Jan 21, 2010 #7

    Mark44

    Staff: Mentor

    Re: Domain

    Yes, pretty much. You can say it a little nicer as
    [tex]\{(x, y, z)\in R^3 | y + z \neq 0\}[/tex].
     
  9. Jan 21, 2010 #8
    Re: Domain

    that looks nice thanks
     
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