If f:R→R is defined by fx=x5 for x∈R, where [y] denotes the greatest integer not exceeding y, then fx:x<71=

fx=x5if x<71⇒ −71<x<71⇒ −715<x5<715⇒ 14.2<x5<14.2∴ −15≤x5≤14∴ Range =−15, −14,...,0,...,13,14

If f:R→R is defined by fx=x5 for x∈R, where [y] denotes the greatest integer not exceeding y, then fx:x<71=

fx=x5if x<71⇒ −71<x<71⇒ −715<x5<715⇒ 14.2<x5<14.2∴ −15≤x5≤14∴ Range =−15, −14,...,0,...,13,14

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$I f f : R \to R i s d e f i n e d b y f (x) = [\frac{x}{5}] f o r x \in R,$ where [y] denotes the greatest integer not exceeding y, then $\{f (x) : |x| < 71\} =$

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$\{- 14, - 13, ...., 0, ..., 13, 14\}$

$\{- 14, - 13, ...., 0, ..., 13, 14, 15\}$

$\{- 15, - 14, ...., 0, ..., 13, 14\}$

$\{- 15, - 14, ...., 0, ..., 14, 15\}$

answer is C.

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Detailed Solution

$\begin{array}{l} f (x) = [\frac{x}{5}] \\ i f |x| < 71 \\ \Rightarrow - 71 < x < 71 \\ \Rightarrow \frac{- 71}{5} < \frac{x}{5} < \frac{71}{5} \\ \Rightarrow 14.2 < \frac{x}{5} < 14.2 \\ ∴ - 15 \leq [\frac{x}{5}] \leq 14 \\ ∴ R a n g e = \{- 15, - 14, ..., 0, ..., 13, 14\} \end{array}$