The function \(f : x \mapsto 6 - 4\cos\left(\frac{1}{2}x\right)\) is defined for \(0 \leq x \leq 2\pi\).

1. Find the exact value of \(x\) for which \(f(x) = 4\). [3]
2. State the range of \(f\). [2]
3. Sketch the graph of \(y = f(x)\). [2]
4. Find an expression for \(f^{-1}(x)\). [3]