Question

Which of the following functions has finite number of points of discontinuity in $R$ (where $[\cdot ]$ denotes greatest integer)

• A. $\tan x$
• B. $\frac{\left|x\right|}{x}$
• C. $x+\left[x\right]$
• D. $\sin \left(\pi x\right)$

Answer 1

The correct option is B $\frac{\left|x\right|}{x}$

$f\left(x\right)=\tan x$ as $tanx$ is periodic
function and it is discontinuous at odd multiples
of $\frac{\pi }{2}$ So it has not have
finite number of discontinuity points
$f\left(x\right)=\{\begin{array}{c}1x>0\\ -1x<0\\ 0x=0\end{array}$

So it has a finite number of discontinuity
points
$f\left(x\right)=x+\left[x\right]$ It is discontinuous at integer
points
$f\left(x\right)=\sin \left(\pi x\right)$ It is continuous
function