Let be defined by

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

Problem

Let

f:[0,3]\to\mathbb{R}

be defined by

f(x)=\min\{x-[x],1+[x]-x\}

, where

[x]

is the greatest integer less than or equal to

x

. Let

P

denote the set containing all

x\in[0,3]

where

f

is discontinuous, and

Q

denote the set containing all

x\in(0,3)

where

f

is not differentiable. Then the sum of the number of elements in

P

and

Q

is equal to (a) 5 (b) 3 (c) 6 (d) 2