Let \(g:N\to N\) be defined as \(\begin{matrix}g(3n+1)=3n+2, \\ g(3n+2)=3n+3, \\ g(3n+3)=3n+1,\text{ for all }n\geq 0\en…

There exists a function \(f: N \rightarrow N\) such that gof \(=f\)

\(\operatorname{gog} \circ \mathrm{g}=g\)

There exists a one-one function \(f: N \rightarrow N\) such that fog \(=f\)

There exists an onto function \(f: N \rightarrow N\) such that \(f \circ g=f\)