At how many points is the function f(x) = [x] discontinuous?

  1. 1
  2. 2
  3. 3
  4. Infinite

Answer (Detailed Solution Below)

Option 4 : Infinite
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Detailed Solution

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Explanation:

To find the point of discontinuity of the function f(x) = [x], draw the graph of the function f(x) = [x].

Greatest Integer Function: (Floor function)

The function f (x) = [x] is called the greatest integer function and means greatest integer less than or equal to x i.e [x] ≤ x.

The domain of [x] is R and range is I, where R is the set of real numbers and I is the set of integers.

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From the graph, we can say that the function is discontinuous at every integer.

Hence, the function f(x) = [x] discontinuous is at infinite points.

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