Question

If $f:R\to R$ is defined by $f\left(x\right)=\left[\frac{x}{5}\right]$ for $x\in R$, where $\left[y\right]$ denotes the greatest integer not exceeding $y$, then $\left\{f\right(x):|x|<71\}=$

• A. $\{-14,-13,.....,0,.....13,14\}$
• B. $\{-14,-13,.....,0,.....14,15\}$
• C. $\{-15,-14,.....,0,.....14,15\}$
• D. $\{-15,-14,.....,0,.....13,14\}$

Answer 1

The correct option is D $\{-15,-14,.....,0,.....13,14\}$

We have $|x|<71\Rightarrow -71<x<71$

Hence $\left[\frac{-71}{5}\right]<\text{f}\left(x\right)<\left[\frac{71}{5}\right]$

$\Rightarrow [-14.2]<\text{f}\left(x\right)<\left[14.2\right]$

$\Rightarrow -15\le \text{f}\left(x\right)\le 14$,

Also output of $\text{f}\left(x\right)$ will be an integer