A function f is defined by \(f : x \mapsto 3 \cos x - 2\) for \(0 \leq x \leq 2\pi\).

1. Solve the equation \(f(x) = 0\). [3]
2. Find the range of \(f\). [2]
3. Sketch the graph of \(y = f(x)\). [2]

A function g is defined by \(g : x \mapsto 3 \cos x - 2\) for \(0 \leq x \leq k\).

1. State the maximum value of \(k\) for which \(g\) has an inverse. [1]
2. Obtain an expression for \(g^{-1}(x)\). [2]