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

Options

A. `(|x|)/(x)`
B. `x *[x]`
C. tan x
D. `sin[n pi x]`

Answer

A

Explanation

Here, x[x] is discontinuous, when x = k and `k in Z`.
`tan x` is discontinuous, when `x=(2n+1)(pi)/(2), n in Z`
and `sin [n pi x]` is discontinuous, when `n pi x = m, m in Z.`
So, all the above functions have infinite number of points of discontinuity, whereas `(|x|)/(x)` is ciscontinuous, when x = 0 only and have finite number of points of discontinuity.