Question

Find the set of values of x for which it satisfies $-2\le \left[x\right]\le 4.$ (where $\left[\right]$ denotes the greatest integer function )

• A. $[-2,5)$
• B. $(-2,5]$
• C. $(-2,5)$
• D. $[-2,5]$

Answer 1

Answer: (A)

$[-2,5)$

Given $-2\le \left[x\right]\le 4$

As we know for$\left[x\right]\ge n\Rightarrow x\ge n$ for $n\in Z$

and for $\left[x\right]\le n\Rightarrow x<n+1$ for$n\in Z$

$\Rightarrow \left[x\right]\ge -2$ and $\left[x\right]\le 4$

$\Rightarrow x\ge -2$ and $x<(4+1)$

$\Rightarrow x\ge -2$ and $x<5$

$\Rightarrow -2\le x<5$

$\therefore x\in [-2,5)$