The diagram shows the function \(f\) defined for \(0 \leq x \leq 6\) by:

\(x \mapsto \frac{1}{2}x^2\) for \(0 \leq x \leq 2\),

\(x \mapsto \frac{1}{2}x + 1\) for \(2 < x \leq 6\).

(i) State the range of \(f\).

(ii) Copy the diagram and on your copy sketch the graph of \(y = f^{-1}(x)\).

(iii) Obtain expressions to define \(f^{-1}(x)\), giving the set of values of \(x\) for which each expression is valid.