The function g is such that \(g(x) = 8 - (x - 2)^2\), for \(k \leq x \leq 4\), where \(k\) is a constant.

(ii) State the smallest value of \(k\) for which \(g\) has an inverse.

For this value of \(k\),

(iii) find an expression for \(g^{-1}(x)\),

(iv) sketch, on the same diagram, the graphs of \(y = g(x)\) and \(y = g^{-1}(x)\).