(a) The functions \(f : x \to x^{2} + 1\) and \(g : x \to 5 - 3x\) are defined on the set of the real numbers, R.

(i) State the domain of \(f^{-1}\), the inverse of f ; (ii) find \(g^{-1} (2)\).

(b) Evaluate : \(\int \frac{(x + 3)}{x^{2} + 6x + 9} \mathrm {d} x\)