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JEE Main202312 Apr 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let x be the greatest integer ≤ x . Then the number of points in the interval ( – 2 , 1 ) where the function f x = x + x - x is discontinuous, is _____.

Correct answer

0

Step-by-step solution

Given, f x = x + x - x x - x ≥ 0 ⇒ x ∈ R Now using the property of greatest integer function and simplifying the function we get, f x = 2 + x + 2 ,     - 2 < x < - 1 1 + x + 1 ,       - 1 ≤ x < 0 x ,               0 ≤ x < 1   Now plotting the diagram we get, Now from the diagram we can say that, f x is discontinuous at two points x = – 1 ,   0 .

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