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Homework Help: Find the domain of the function

  1. Feb 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Find domain of f(x, y) = ln ((x2+2x+y2) / (x2−2x+y2))

    2. Relevant equations

    3. The attempt at a solution
    Because the function is a natural ln, the restriction on the function is that everything inside the brackets has to >0, otherwise the function is undefined.

    I worked on the problem for a while but wasn't getting anywhere so i plugged the equation into wolfram and got the domain { (x,y) ∈ R2 | 4x2 < (x2 + y2)2}

    I'm not sure how to get there though...

    [(x2+2x+y2) / (x2−2x+y2)] > 0
  2. jcsd
  3. Feb 24, 2016 #2


    Staff: Mentor

    Because of the natural log, ##\frac{x^2 + 2x + y^2}{x^2 - 2x + y^2}## has to be positive, but you're forgetting that there is a restriction on the denominator.
  4. Feb 24, 2016 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    First, note that for a fixed ##y## you have two quadratics in ##x##. Perhaps start by analysing those quadratics.
  5. Feb 24, 2016 #4

    Ray Vickson

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    Science Advisor
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    So, if ##(x^2+2x+y^2)/(x^2-2x+y^2)>0##, then the numerator and denominator must both be > 0 or both be < 0. It might help to look at those two cases separately.
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