Question

The number of discontinuities of the greatest integer function f(x) = [x], x ∈ `(- 7/2, 100)` is equal to ______.

Options

• 104

• 100

• 102

• 103

Answer 1

The number of discontinuities of the greatest integer function f(x) = [x], x ∈ `(- 7/2, 100)` is equal to 103.

Explanation:

Given, f(x) = [x], x e (-3.5, 100)

As we know greatest integer function is discontinuous on integer values.

In given interval, the integer values are
(- 3, - 2, - 1, 0, .... , 99).

∴ the total number of integers are 103.