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KCET2010MathematicsContinuity and Differentiability

The function f(x)=[x] , where [x] denotes the greatest integer not greater than x , is

Options

  1. Acontinuous for all non-integral values of x
  2. Bcontinuous only at positive integral values of x
  3. Ccontinuous for all real values of x
  4. Dcontinuous only at rational values of x

Correct answer

A. continuous for all non-integral values of x

Step-by-step solution

Given, f(x)=[x] from the graph we observe that f(x)=[x] discontinuous at every integral value of x . That means, f(x)=[x] . Continuous only for all non-integral values of x .

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