Functions f and g are defined for \(x \in \mathbb{R}\) by

\(f : x \mapsto \frac{1}{2}x - 2\),

\(g : x \mapsto 4 + x - \frac{1}{2}x^2\).

(i) Find the points of intersection of the graphs of \(y = f(x)\) and \(y = g(x)\).

(ii) Find the set of values of \(x\) for which \(f(x) > g(x)\).

(iii) Find an expression for \(fg(x)\) and deduce the range of \(fg\).

The function \(h\) is defined by \(h : x \mapsto 4 + x - \frac{1}{2}x^2\) for \(x \geq k\).

(iv) Find the smallest value of \(k\) for which \(h\) has an inverse.