The function \(f : x \mapsto 5 + 3 \cos\left(\frac{1}{2}x\right)\) is defined for \(0 \leq x \leq 2\pi\).

1. Solve the equation \(f(x) = 7\), giving your answer correct to 2 decimal places. [3]
2. Sketch the graph of \(y = f(x)\). [2]
3. Explain why \(f\) has an inverse. [1]
4. Obtain an expression for \(f^{-1}(x)\). [3]