Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f(x) = 
([.] denotes the greatest integer function), then f(x) is
A
Discontinuous at some x
B
Continuous at all x, but the derivative 
doesn’t exist for some x
doesn’t exist for some x
C
f ′ ′ (x) exists for all x, but f ′ ′ ′ ′ (x) doesn’t exist some x
D
f ′ ′ ′ ′ (x) exist for all x
Text Solution
Verified by ExpertsThe correct answer is:
D
Since 
is an integer whatever be the value of x and so 2 π π 
is an integral multiple of π π .
Thus, sin (2 π π [ π π 2 x]) = 0 and 5 + [x] 2 ≠ ≠ 0 for all x.
Hence f(x) = 0 ∀ ∀ x ∈ ∈ R.
Thus, f(x) is a constant function and so it is continuous and differentiable any number of times for all x ∈ ∈ R
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