Let . The set of real solutions of the equation…

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

Problem

Let q(x)=⌊x⌋2−sgn⁡(x) ⌊x⌋q(x)=\lfloor x\rfloor^{2}-\operatorname{sgn}(x)\,\lfloor x\rfloor. The set of real solutions of the equation q(x)=2q(x)=2 is (a) [−2,−1)∪[1,2)[-2,-1)\cup[1,2) (b) (−2,−1]∪[2,3)(-2,-1]\cup[2,3) (c) [−2,−1)∪[2,3)[-2,-1)\cup[2,3) (d) [−1,0)∪[2,3)[-1,0)\cup[2,3)

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