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MHT CET20225 Aug 2022Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f ( x )= x 2 -1 , then on the interval [0, ] where [.] represents greatest integer function

Options

  1. A[ f ( x )] is continuous but 1 f ( x ) is not continuous.
  2. B[ f ( x )] and 1 f ( x ) are both continuous.
  3. C[ f ( x )] and 1 f ( x ) are both discontinuous.
  4. D[ f ( x )] is discontinuous and 1 f ( x ) is continuous.

Correct answer

C. [ f ( x )] and 1 f ( x ) are both discontinuous.

Step-by-step solution

[ f ( x )]= [ x 2 -1 ]= array lll (-1), & if & 0 x <2 (0)=0, & if & 2 x array . which is discontinuous at x =2 1 f(x) = 1 x 2 -1 which is discontinuous at x=2

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