Let denote the greatest integer less than or equal to

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

Problem

Let [t][t] denote the greatest integer less than or equal to tt. The number of points where the function f(x)=[x]x2−1+sin⁡(π[x]+3)−[x+1]f(x)=[x]x^2-1+\sin\left(\frac{\pi}{[x]+3}\right)-[x+1], x∈(−2,2)x\in(-2,2), is not continuous is (a) 1 (b) 2 (c) 4 (d) 3

Related theory

Browse the problem library