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

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

Aicharya · Accepted Answer

Given, $f: R ightarrow R$ and $f(x)=\left[\frac{x}{5}ight]$ Also, $\begin{aligned} & \{f(x):|x| < 71\}=\{f(x):-71 < x < 71\} \ & =\left\{\left[\frac{x}{5}ight]:-71 < x < 71ight\} \ & \left\{\left[\frac{-70-0.1}{5}ight], \ldots,\left[\frac{-70}{5}ight], \ldots,\left[\frac{0}{5}ight],ight. \ & \left.\ldots,\left[\frac{65}{5}ight], \ldots,\left[\frac{70}{5}ight], \ldots,\left[\frac{70+0.999}{h}ight]ight\} \ & =\{-15,-14, \ldots, 0, \ldots, 13,14\} \end{aligned}$

If $f: R \rightarrow R$ is defined by $f(x)=\left[\frac{x}{5}\right]$ for $x \in R$, where $[y]$ denotes the…

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