Question

For the function $f\left(x\right)=\left[x\right]+[-x]$ which among the following options is TRUE

• A. $f\left(x\right)$ has Finite type discontinuity
• B. $f\left(x\right)$ has Isolated point discontinuity
• C. $f\left(x\right)$ has Missing point discontinuity
• D. $f\left(x\right)$ has Infinite type discontinuity

Answer 1

The correct option is B $f\left(x\right)$ has Isolated point discontinuity

$f\left(x\right)=\left[x\right]+[-x]=\{\begin{array}{cc}0& \text{if}x\in I\\ -1& \text{if}x\notin I\end{array}$
Clearly, $f\left(x\right)$ has isolated point of discontinuity at all integral points.