Let $\displaystyle f(x,y) $ be a periodic function such that $\displaystyle f(x,y) = f((2x-2y),(2y-2x)) \forall \ x, \ y \epsilon R $. Define $\displaystyle g(x) = f(2^x,0) $. Prove that $\displaystyle g(x) $ is periodic and find its period.

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- Jul 22nd 2010, 10:03 AMsashikanthPeriodic function of 2 variables
Let $\displaystyle f(x,y) $ be a periodic function such that $\displaystyle f(x,y) = f((2x-2y),(2y-2x)) \forall \ x, \ y \epsilon R $. Define $\displaystyle g(x) = f(2^x,0) $. Prove that $\displaystyle g(x) $ is periodic and find its period.

- Jul 24th 2010, 03:41 AMtonio
- Jul 24th 2010, 03:54 AMsashikanth
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:

$\displaystyle 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:

$\displaystyle 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. :)