A) \[\operatorname{tanx}\]
B) \[x[x]\]
C) \[\frac{\left| x \right|}{x}\]
D) \[\sin [\pi x]\]
Correct Answer: C
Solution :
[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\[f(x)=\frac{\left| x \right|}{x}\]is discontinuous when x=0 only.
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