Let f:[0,3] → 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 [0, 3] where f i discontinuous, and Q denote the set containing all x (0, 3) where f is not differentiable. Then the sum of number of elements in P and Q is equal to _ _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Morning shift · Q41

JEE Main 202127 Jul, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let

f:[0,3] \to 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 i discontinuous, and Q denote the set containing all x

\in

(0, 3) where f is not differentiable. Then the sum of number of elements in P and Q is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Limit, Continuity and Differentiability Question with Answer (27 Jul Morning shift, Q41) | JEE Arc