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

Question

The number of points of discontinuity of the greatest integer function f(x)=[x], x∈ (- (7/2) , 100) is equal to (A) 104 (B) 102 (C) 101 (D) 103

Tardigrade Admin · Accepted Answer

Given, f(x)=[x], x∈ (- 3.5 , 100) As we know the greatest integer function [x] is discontinuous at all integer values of x In given interval, the integer values are .-3, -2, -1, 0, ldots , 99. ∴ Total numbers of integers are 103 .

Q. The number of points of discontinuity of the greatest integer function $f (x) = [x], x \in (- \frac{7}{2}, 100)$ is equal to

$104$

$102$

$101$

$103$

Given, $f (x) = [x], x \in (- 3.5, 100)$
As we know the greatest integer function $[x]$ is discontinuous at all integer values of $x$
In given interval, the integer values are
${- 3, - 2, - 1, 0, \dots, 99}$
$∴$ Total numbers of integers are $103$ .

Q. The number of points of discontinuity of the greatest integer function f(x)=[x],x∈(−27​,100) is equal to

104

102

101

103