JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q2

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MathematicsSingle correct+4 / -1Question 2 of 90

Let a function $f:\mathbb N\to\mathbb N$ be defined by
$f(n)=\begin{cases}2n, & n=2,4,6,8,\dots\\ n-1, & n=3,7,11,15,\dots\\ \dfrac{n+1}2, & n=1,5,9,13,\dots\end{cases}$
then, $f$ is

one-one but not onto

onto but not one-one

neither one-one nor onto

one-one and onto

Answer and worked solution

Official answer: D

Images. Even $n$ go to multiples of 4; $n\equiv3\pmod4$ go to numbers $\equiv2\pmod4$ ; $n\equiv1\pmod4$ go to $1,3,5,\dots$ , every odd number once.

The three pieces are one-one and together cover $\mathbb N$ exactly once.

(D)

Topics:Types of functions

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JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 2