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=

−71<x<71 ⇒−715<x5<715⇒−14.5<x5<14.5 ⇒x∈−15,−14.......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=

−71<x<71 ⇒−715<x5<715⇒−14.5<x5<14.5 ⇒x∈−15,−14.......13,14

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

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

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

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

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

answer is A.

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Detailed Solution

$- 71 < x < 71 \Rightarrow \frac{- 71}{5} < \frac{x}{5} < \frac{71}{5} \Rightarrow - 14.5 < \frac{x}{5} < 14.5 \Rightarrow [x] \in \{- 15, - 14.......13, 14\}$

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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=

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