Question

The domain of the function $f\left(x\right)=\sqrt{3+2\left[x\right]-[x{]}^2},$ where $[.]$ represents the greatest integer function is

• A. $(-2,4)$
• B. $[-1,3]$
• C. $(-2,3]$
• D. $[-1,4)$

Answer 1

The correct option is D $[-1,4)$

$3+2\left[x\right]-[x{]}^2\ge 0$
$\Rightarrow [x{]}^2-2[x]-3\le 0$
$\Rightarrow \left(\right[x]+1)\left(\right[x]-3)\le 0$
$\Rightarrow -1\le \left[x\right]\le 3$
$\Rightarrow -1\le x<4$