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

Given function is  $f\left(n\right)=\left\{\begin{array}{l}2n ; n=2,4,6,8,...\\ n-1 ;n=3,7,11,15,...\\ \frac{n+1}{2} ;n=1,5,9,...\end{array}\right.$

When n = 2, 4, 6 then 2n Is the multiple of 4
When n = 3, 7, 11, 15 then (n-1) is not multiple of 4
When n=1, 5,9,13, then  $\left(\frac{n+1}{2}\right)$ is the odd number
Every number gives exactly one value
Thus, f is one-one & onto