Question

Which of the following functions have finite number of points of discontinuity in R ([•] represents the greatest integer function)?

• A. $tan \,x$
• B. $x [x]$
• C. $\frac{|x|}{x}$
• D. $sin [\pi x]$

Answer 1

Answer: (C)

$f (x) = tan x$ is discontinuous when $x=(2n+1) \pi/2$, $n \in\,z$
$f (x) = x [x]$ is discontinuous when $x=k$, $k\, \in\,z$
$f (x)=sin [n \pi x]$ is discontinuous when $n\,\pi x=k, k \in\,z$
Thus, all the above functions have infinite number of points of discontinuity
But $f (x) =\frac{|x|}{x}$ is discontinuous when $x = 0$ only