Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Discuss the continuity of the function f(x) given by f(x) = [x] + [–x] at integer points.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. [–x] = 
∴ f(x) = [x] + [–x] = 
Now let 'a' be an arbitrary integer. Then,
f(x) = 
f(a – h) = 
–1 = –1
f(x) = 
f(a+ h) = 
–1 = –1 and f(a) =0
∴ lim f(x) = 
f(x) ≠ f(a) ⇒ f(x)
is discontinuous at x = a
Therefore f(x) is discontinuous at integer points.
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