Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
1771 Upvotes
Verified Answer
The correct answer is:
$\{-15,-14, \ldots, 0, \ldots, 13,14\}$
Given, $f: R \rightarrow R$ and $f(x)=\left[\frac{x}{5}\right]$
Also,
$\begin{aligned}
& \{f(x):|x| < 71\}=\{f(x):-71 < x < 71\} \\
& =\left\{\left[\frac{x}{5}\right]:-71 < x < 71\right\} \\
& \left\{\left[\frac{-70-0.1}{5}\right], \ldots,\left[\frac{-70}{5}\right], \ldots,\left[\frac{0}{5}\right],\right. \\
& \left.\ldots,\left[\frac{65}{5}\right], \ldots,\left[\frac{70}{5}\right], \ldots,\left[\frac{70+0.999}{h}\right]\right\} \\
& =\{-15,-14, \ldots, 0, \ldots, 13,14\}
\end{aligned}$
Also,
$\begin{aligned}
& \{f(x):|x| < 71\}=\{f(x):-71 < x < 71\} \\
& =\left\{\left[\frac{x}{5}\right]:-71 < x < 71\right\} \\
& \left\{\left[\frac{-70-0.1}{5}\right], \ldots,\left[\frac{-70}{5}\right], \ldots,\left[\frac{0}{5}\right],\right. \\
& \left.\ldots,\left[\frac{65}{5}\right], \ldots,\left[\frac{70}{5}\right], \ldots,\left[\frac{70+0.999}{h}\right]\right\} \\
& =\{-15,-14, \ldots, 0, \ldots, 13,14\}
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.