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IAT IISER2025MathematicsContinuity and Differentiability

Let f: R R be defined as f(x)= |x^3-3 x |[x] , where [x] denotes the greatest integer less than or equal to x . Which one of the following statements is TRUE?

Options

  1. AEvery non-zero integer is a point of discontinuity of f
  2. Bf is continuous at every real number
  3. CEvery integer is a point of discontinuity of f
  4. Df is continuous at every real number except for 0, 3

Correct answer

A. Every non-zero integer is a point of discontinuity of f

Step-by-step solution

No Solution

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