Question

Find the number of points of discontinuity for $f\left(x\right)=\left[6\sin x\right],0\le x\le \pi$ (Where $[.]$ denotes the greatest integer function)

Answer 1

$f\left(x\right)=\left[6\sin x\right],0\le x\le \pi$ ($[.]$ is G.I.F.)

Range of $\sin x$ is $[0,1]$, when $xϵ[0,\pi ]$

Then range of $6\sin x$ is $[0,6]$

As $f\left(x\right)$ is a G.I.F, it is discontinuous at all integers in its domain, domain of $f\left(x\right)$is range of $6\sin x$

$\Rightarrow$No. of points of discontinuity=no. of integers in $[0,6]$

$=7$