Question

The range of the function $f\left(x\right)=\frac{\sin \left(\pi \right[x\left]\right)}{x^2+1}$ (where $[.]$ denotes greatest integer function) is

• A. $\left\{0\right\}$
• B. $R$
• C. $(0,1)$
• D. $(0,\infty )$

Answer 1

The correct option is A $\left\{0\right\}$

$f\left(x\right)=\frac{\sin \left(\pi \right[x\left]\right)}{x^2+1}$
$\because$ $\left[x\right]$ always gives integer value and $\sin n\pi =0$
$\therefore f\left(x\right)=0$