Let a function $f:N \to N$ be defied by $f\left( n \right) = \left[ {\begin{array}{*{20}{c}} {2n,}&{n = 2,4,6,8....} \\ {n - 1,}&{n = 3,7,11,15....} \\ {\frac{{n + 1}}{2},}&{n = 1,5,9,13....} \end{array}} \right.$ then $f$ is

JEE MATHEMATICS MCQ: FUNCTIONS

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Let a function

f:N \to N

be defied by

f\left( n \right) = \left[ {\begin{array}{cccccccccccccccccccc} {2n,}&{n = 2,4,6,8....} \\ {n - 1,}&{n = 3,7,11,15....} \\ {\frac{{n + 1}}{2},}&{n = 1,5,9,13....} \end{array}} \right.

then

f

View answer and explanation

Correct option: D

One-one and onto

Option D (One-one and onto) is correct because the function covers all natural numbers in its range and each element in the domain maps to a unique element in the range.

JEE MATHEMATICS MCQ: FUNCTIONS

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