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

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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