Consider the function \(g:\Z \to \Z\) defined by \(g(n) = n^2 + 1\text{.}\) Find \(g(1)\) and \(g(\{1\})\text{.}\) Then find \(g\inv(1)\text{,}\) \(g\inv(2)\text{,}\) and \(g\inv(3)\text{.}\)