JEE Main 2022 (Online) 28th June Morning ShiftQuestion 1
Let a function $f:\mathbf{N}\to\mathbf{N}$ be defined by $f(n)=\begin{cases}2n, & n=2,4,6,8,\ldots\\ n-1, & n=3,7,11,15,\ldots\\ \frac{n+1}{2}, & n=1,5,9,13,\ldots\end{cases}$ then, $f$ is
Functions
Solution
Evens give multiples of $4$, $n\equiv3\pmod4$ give $2,6,10,\dots$, $n\equiv1\pmod4$ give all odd numbers; the images are disjoint and cover $\mathbb N$, so $f$ is one-one and onto.