Suppose that \(f(x) = ax + b\) and \(g(x) = f^{-1}(x)\) for all values of \(x\). That is, \(g\) is the inverse of the function \(f\).
If \(f(x) - g(x) = 2022\) for all values of \(x\), determine all possible values for \(a\) and \(b\).
