If f(x) = [x] - [ x 4 ], x R where [x] denotes the greatest integer less than or equal to x, then

MHT CET 2022 Mathematics question

If , where denotes the greatest integer less than or equal to x, then

(A) exists, but does not exist.
(B) is continuous at Correct
(C) exists, but does not exist
(D)Both and exist, but are not equal

Answer: (B)

Solution

At : . Left-hand limit: for x slightly less than 4, and (as is slightly less than 1), so . Right-hand limit: for x slightly more than 4, and \frac{x}{4}$]

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Question ID VK-095970