Question

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

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

Answer 1

Answer: (C)

$f(x)=tanx$ 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