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NDA2017MathematicsContinuity and DifferentiabilityActual

If f(x)= x 2 -1 , then on the interval [0, ] which one of the following is correct?

Options

  1. A[f(x)] , where [ ] is the greatest integer function, and 1 f( x ) are both continuous.
  2. B[f(x)] , where [ ] is the greatest integer functin, and f⁻¹( x ) are both continuous.
  3. C[f(x)] , where [ ] is the greatest integer function, and 1 f( x ) are both discontinuous.
  4. D[f(x)] , where [ ] is the greatest integer function, is discontinuous but 1 f( x ) is continuous.

Correct answer

C. [f(x)] , where [ ] is the greatest integer function, and 1 f( x ) are both discontinuous.

Step-by-step solution

aligned & f ( x )= x 2 -1, [0, ] & f ( x )= ( x 2 -1 ) aligned 1 f(x) = 1 x 2 -1 is discontinuous at x=2 . f ( x ) is discontinuous for x =2 in [0, ]

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