Determine all real numbers that satisfy

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Determine all real numbers xx that satisfy h(x)=1h(x)=1, where h(x)=⌊x2⌋+sgn⁡(3−x)h(x)=\left\lfloor\dfrac{x}{2}\right\rfloor+\operatorname{sgn}(3-x).

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