If f:N→Z is defined by $f\left( n \right) = \left\{ {\begin{array}{*{20}{c}} {2\;\;\;if\;\;\;n\; = \;3k,\;k \in Z}\\ {10\;\;if\;n = 3k + 1,\;k \in Z,}\\ {0\;if\;n = 3k + 2,\;k \in Z} \end{array}} \right.$ Then $\{ n \in N:f\left( n \right) > 2\} $ is equal to

$\left\{ {1,{\rm{ }}4,{\rm{ }}7} \right\}$

$\left\{ {3,{\rm{ }}6,{\rm{ }}4} \right\}$

$\left\{ {4,{\rm{ }}7} \right\}$

JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

If f:N→Z is defined by

f\left( n \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {2\;\;\;if\;\;\;n\; = \;3k,\;k \in Z}\\ {10\;\;if\;n = 3k + 1,\;k \in Z,}\\ {0\;if\;n = 3k + 2,\;k \in Z} \end{array}} \right.

Then

\{ n \in N:f\left( n \right) > 2\}

is equal to

View answer and explanation

Correct option: B

\left\{ {1,\mathrm{ }4,\mathrm{ }7} \right\}

Option B (

\{ 1,\;4,\;7 \}

) is correct because these are the values of n for which f(n) > 2 based on the given piecewise function.