The function defined by ;

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The function gg defined by g(x)=sin⁡α+cos⁡α−1g(x) = \sin \alpha + \cos \alpha - 1 ; α=sin⁡−1{x}\alpha = \sin^{-1} \sqrt{\{x\}} , where {x}\{x\} denotes fractional part function, is (1) an even function (2) periodic function (3) odd function (4) neither even nor odd

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