Question

$f\left(x\right)=\frac{1}{x-\left[x\right]}$. Find points of discontinuity.

• A. all rational numbers
• B. $x=0$
• C. Whole numbers
• D. Integers

Answer 1

Answer: (B), (C)

The correct options are
B $x=0$
C Whole numbers

The functions are not defined for $x=0$ and for natural values of $x$ as $\left[x\right]=x.$
$\therefore x=0$ and natural values of $x$ are all points of discontinuity.