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CGP EDU Academic Team
Published on: August 14, 2026
If f(x) = x + { − x} + [x], where [ . ] is the integral part & { . } is the fractional part function. Discuss the continuity of f in [ − 2, 2 ]. Also find nature of each discontinuity.
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discontinuous at all integral values in [ − 2, 2]
Sol. f(x) = x + {–x} + [x] Since {–x} = 
= 
= 
Curve of y = f(x)
discontinuous at all integers in [–2, 2]
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