Published by:
CGP EDU Academic Team
Published on: August 12, 2026
The function f(x) = [x] cos 
π , (where [.] denotes the greatest integer function) is discontinuous at -
A
All x
B
x = 
, n ∈ I – {1}
, n ∈ I – {1}
C
x ∈ N
D
x ∉ I – {0}
Text Solution
Verified by ExpertsThe correct answer is:
B
Case I : when x ∈ n,
then f(x) = x cos 
π
f(n) = n cos (n – 1) π
f(x) = n cos(n – 1) π
f(x) = (n – 1) cos(n – 1) π
limit exist if cos (n – 1) π = 0 which is not
possible.
f(x) is discontinuous at all x ∈ I.
Case II : when x is not integer
Let 
= m, m is integer, then
x = 
= m + 
= m cos (m – 1) π
= m cos m π
limit exist only when m = 0 i.e. n = 
Hence discontinuous at x = 
, n ∈ I – {1}.
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