2026 May AASL TZA Paper 1 Q6

The function \(f\) is defined by \(f(x) = 4 - \frac{7}{3x + 2}\), where \(x \in \mathbb{R}, x \neq -\frac{2}{3}\).

1. Find an expression for \(f^{-1}(x)\).

   [3]

The function \(g\) is defined such that \( (f \circ g) \left( \frac{x}{3} \right) = x\).

2. Using your answer to part (a) or otherwise, find an expression for \(g(x)\).

   [3]