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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) = [x] and g(x) = 0 when x is an integer and g(x) = x^2 when x is not an integer ( [ ] is the greatest integer function) then :

Options

  1. A_ x 1 g(x) exists, but g(x) is not continuous at x = 1
  2. B_ x 1 f(x) does not exist
  3. Cgof is continuous for all x
  4. Dfog is continuous for all x

Correct answer

A. _ x 1 g(x) exists, but g(x) is not continuous at x = 1

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