Question

The number of points at which the function $f\left(x\right)=\frac{1}{(x-[x\left]\right)}$ is not continuous is

• A. $1$
• B. $2$
• C. $3$
• D. none of these

Answer 1

The correct option is D

none of these

Finding continuity of function:

Given $f\left(x\right)=\frac{1}{(x-[x\left]\right)}$

The greatest integer function becomes discontinuous at every integer value of$x.$ So, the whole function will become discontinuous at each integer value of$x.$

It will have infinite number of points of discontinuity.

Hence, option (D) is the answer.