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Math Olympiads problem

  1. Dec 10, 2011 #1
    1. The problem statement, all variables and given/known data

    [tex]f\left(x^{2}+f(y)\right)=y-x^{2}[/tex]


    2. Relevant equations

    Find all functions f that satisfy the relationship for every real x and y.

    3. The attempt at a solution

    is this correct reasoning?

    for x=0: [tex]f(y)=f^{-1}(y)[/tex]

    for x>0: [itex]\existsxεℝ[/itex]: [tex]x=k^{2}[/tex]

    [tex]f(k^{2}+f(0))=-k^{2}+f(0)[/tex]

    for x<0 [itex]\existsxεℝ[/itex]: [tex]x=-k^{2}[/tex]

    [tex]f(0)=f(k^{2}+f(-k^{2}))[/tex] = [tex]f(-k^{2})-k^{2}[/tex] which entails:

    [tex]f(-k^{2})=f(0)+k^{2}[/tex] =[tex]-(-k^{2})+f(0)[/tex]
     
  2. jcsd
  3. Dec 10, 2011 #2

    SammyS

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    This question has been previously discussed.

    http:
    //www.physicsforums.com/showthread.php?t=556487


    Is there anything new in what you're posting this time?
     
  4. Dec 10, 2011 #3
    yes for x>0 and for x<0 i want to know if what i did is correct.
     
  5. Dec 10, 2011 #4

    micromass

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    Please post in the old thead.
     
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