Find the period!

Algebra Level 5

\[ \large f(x,y) = f((2x+2y), (2y-2x)) \]

For all real values of \(x\) and \(y\), consider a periodic function \(f(x,y) \) that satisfies the equation above.

Suppose we define a function \(g\) by \(g(x) = f(2^x,0) \), what is the period of \(g(x) \)?

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