JEE MAIN - Mathematics (2021 - 27th July Morning Shift - No. 25)

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 ______________.
Answer
5

Explanation



1 $$-$$ {x} = 1 $$-$$ x; 0 $$\le$$ x < 1



Non differentiable at

$$x = {1 \over 2},1,{3 \over 2},2,{5 \over 2}$$

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