Question

Let $f\left(x\right)=[x^3-3]$, where $\left[x\right]$ is the greatest integer function. Then, the number of points in the interval $(1,2)$, where function is discontinuous, is

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$

$f\left(x\right)=[x^3-3]f\left(x\right)=\left[x^3\right]-3$

Integral part function is discontinuous at integral points

$x\in (1,2)\Rightarrow x^3\in (1,8)$

So $x^3$ becomes $2,3,4,5,6,7$ in $(1,2)$

So the function is discontinuous at $6$ points

Option $C$ is correct.