Find the period!

Algebra Level 5

f(x,y)=f((2x+2y),(2y2x)) \large f(x,y) = f((2x+2y), (2y-2x))

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

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

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