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\includegraphics[max width=\textwidth, alt={}, center]{32a57386-2696-4fda-a3cb-ca0c5c3be432-3_778_816_255_662} The diagram shows the function f defined for \(0 \leqslant x \leqslant 6\) by $$\begin{aligned} & x \mapsto \frac { 1 } { 2 } x ^ { 2 } \quad \text { for } 0 \leqslant x \leqslant 2 ,
& x \mapsto \frac { 1 } { 2 } x + 1 \text { for } 2 < x \leqslant 6 . \end{aligned}$$

1. State the range of f .
2. Copy the diagram and on your copy sketch the graph of \(y = \mathrm { f } ^ { - 1 } ( x )\).
3. Obtain expressions to define \(\mathrm { f } ^ { - 1 } ( x )\), giving the set of values of \(x\) for which each expression is valid.