Let be a function defined by

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

Problem

Let f:(2,4)→(1,3)f:(2,4)\rightarrow(1,3) be a function defined by f(x)=x−[x2]f(x)=x-\left[\frac{x}{2}\right], where [⋅][\cdot] denotes the greatest integer function. Then f−1(x)f^{-1}(x) is equal to: (a) 2x2x (b) x+[x2]x+\left[\frac{x}{2}\right] (c) x+1x+1 (d) x−1x-1

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