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JEE MATHEMATICS MCQ: FUNCTIONS

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On the set of integers Z, define f:Z→Zf:Z \to Z as f(n)={n2,  n    is    even0,      n      is    odd}f\left( n \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {\frac{n}{2},\;n\;\;is\;\;even}\\ {0,\;\;\;n\;\;\;is\;\;odd} \end{array}} \right\}, then ′f′'f' is
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Correct option: D
Surjective but not injective
Option D (Surjective but not injective) is correct because the function maps multiple odd integers to 0, making it not injective, but covers all integers in the range, making it surjective.

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