Let $f(x) = \lfloor x^2 - 3 \rfloor$ where $\lfloor \cdot \rfloor$ is the greatest integer function.
Number of points in $(1,2)$ where $f$ is discontinuous:
🎥 Video solution / Text Solution of this question is given below:
Discontinuity occurs when
$x^2 - 3$ is an integer
Let
$x^2 - 3 = k \Rightarrow x = \sqrt{k+3}$
We need $1 < x < 2$ → square both sides:
$1 < \sqrt{k+3} < 2$