Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f(x)=[x sin π π x], (where [.] denotes the greatest integer function) then f(x) is
Text Solution
Verified by ExpertsThe correct answer is:
A
By the definition of [x], it is obvious that f(x) = [x sin π π x] = 0 when –1 ≤ ≤ x ≤ ≤ 1 and
f(x) = [x sin π π x] = – 1 when 1 < x < 1 + h, (h small) Thus f(x) is constant and equal to 0 in [–1, 1] and hence f(x) is continuous and differentiable in (– 1, 1).
At x = 1, clearly f(x) is discontinuous since 
f(x) = – 1 and 
f(x) = 0
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