Question

If the domain of the function $y=f\left(x\right)$ is $[-3,2],$ then the domain of $f\left(|\right[x\left]|\right)$ is
(where [.] denotes the greatest integer function)

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

Answer 1

The correct option is D $[-2,3)$

The domain of the function $y=f\left(x\right)$ is $[-3,2].$
For $f\left(|\right[x\left]|\right)$ to be defined.
$-3\le |\left[x\right]|\le 2\Rightarrow 0\le |\left[x\right]|\le 2\Rightarrow -2\le \left[x\right]\le 2\therefore x\in [-2,3)$