RADical cyclic function, dude!

Algebra Level 3

If a periodic non-zero function f(x)f(x) exists such that 3f(x)=f(x1)+f(x+1),\sqrt{3}f(x) = f(x - 1) + f(x + 1), which of these options could be its fundamental period?

Note: A function g(x)g(x) is periodic if there exists some TT such that g(x)=g(x+T)g(x) = g(x + T) for all x.x. The fundamental period is the minimum positive TT such that this property holds.

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