JEE Main 2022 Mathematics question

Let a function f : be defined by f(n) = 2n for n = 2, 4, 6, 8, ...; f(n) = n − 1 for n = 3, 7, 11, 15, ...; f(n) = (n + 1)/2 for n = 1, 5, 9, 13, .... then, f is

(1)One-one but not onto
(2)Onto but not one-one
(3)Neither one-one nor onto
(4)One-one and ontoCorrect

Answer: (4)

Solution

For n = 1, 5, 9, 13, …, (n + 1)/2 takes all the odd values 1, 3, 5, 7, …. For n = 3, 7, 11, 15, …, n − 1 takes the values 2, 6, 10, 14, … (even numbers not

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Question ID VK-034957