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JEE Main20205 Sep 2020Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f ( x ) = x · x 2 , for - 10 < x < 10 , where t denotes the greatest integer function. Then the number of points of discontinuity of f x is equal to

Correct answer

0

Step-by-step solution

We know that the greatest integer function is discontinuous at integral points. - 5 < x 2 < 5 ⇒    x 2 = - 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , are the integer values. At x = 0 , f 0 + = f 0 = f 0 - = 0 , which means that function is continuous at x = 0 . ∵ x ≠ - 10 ⇒ x 2 ≠ - 5 Hence, the function is discontinuous at points - 4 , - 3 , - 2 , - 1 , 1 , 2 , 3 , 4 The number of values is 8 .

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