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

Let $g\left(x\right)=x^3-3\text{.}$   Clearly  $g\left(x\right)$ is an increasing 

continuous function on (1, 2) 

we have $g\left(1\right)=-2$ and $g\left(2\right)=5$ 

This means that g (x) assumes all values between - 2 and 

There are 6 integer points between - 2 and 5.  

Thus $\left[x^3-3\right]=\left[g\right(x\left)\right]$  is discontinuous at six integer points.