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

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.

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.