No Problemmo #2

Algebra Level 5

Let \(f(x,y)\) be a periodic function satisfying \(f(x,y) = f( 2x+2y , 2y-2x )\) for all \(x,y\) belonging to the set of real numbers.

Let \(g(x) = f(2^x , 0)\). Then find the fundamental period of \(g(x)\).

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