Question

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

• A. $104$
• B. $102$
• C. $101$
• D. $103$

Answer 1

Answer: (D)

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