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Math Help - Periodic function of 2 variables

  1. #1
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    Periodic function of 2 variables

    Let  f(x,y) be a periodic function such that  f(x,y) = f((2x-2y),(2y-2x)) \forall \ x, \ y  \epsilon R . Define  g(x) = f(2^x,0) . Prove that  g(x) is periodic and find its period.
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  2. #2
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    Quote Originally Posted by sashikanth View Post
    Let  f(x,y) be a periodic function such that  f(x,y) = f((2x-2y),(2y-2x)) \forall \ x, \ y  \epsilon R . Define  g(x) = f(2^x,0) . Prove that  g(x) is periodic and find its period.

    g(x+2)=f(2^{x+2},0)=f(2^{x+3},-2^{x+3})=f(2^{x+1},-2^{x+1})=f(2^x,0)=g(x)

    Tonio
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  3. #3
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    Hi Tonio. Thank you for your reply. I am so sorry, I made an error in posting the question. The actual question in the book reads like this:

     f(x,y) = f((2x+2y),(2y-2x)) \forall \ x, \ y  \ \epsilon \ R

    I do not understand what periodicity of a function of 2 variables means. I tried looking for the definition but I couldn't find it. Also, in your solution, I did not understand this step:

     f(2^{x+2},0)=f(2^{x+3},-2^{x+3})

    I will be very grateful if you could explain it to me. Thank you.
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