Question 42
We consider the set $N=\{1,2,3, \ldots\}$ of the natural numbers and the map $f$ : $N \rightarrow N$ that satisfies the following two conditions:
a) $f(f(n))=n$ for all $n \in N$.
b) $f(f(n)+1)=\left\{\begin{array}{cc}n-1, & \text{and} n \text{are by;} \\ n+3, & \text{and} n \text{is odd.}\end{array}\right.$
Determine the value of $f(n)$ for each $n \in N$ by previously observing that $f$ is bijective and that, since it is never $f(f(n)+1)=2$, it has to be $f(1)=2$.
a) $f(f(n))=n$ for all $n \in N$.
b) $f(f(n)+1)=\left\{\begin{array}{cc}n-1, & \text{and} n \text{are by;} \\ n+3, & \text{and} n \text{is odd.}\end{array}\right.$
Determine the value of $f(n)$ for each $n \in N$ by previously observing that $f$ is bijective and that, since it is never $f(f(n)+1)=2$, it has to be $f(1)=2$.