2007 H2 Mathematics

Paper 1 Question 2

Functions $f$ and $g$ are defined by $\begin{aligned} f : x \mapsto \frac{1}{x - 3} & for x \in ℝ, x \neq 3, \\ g : x \mapsto x^{2} & for x \in ℝ . \end{aligned}$

(a)

Only one of the composite functions $f g$ and $g f$ exists. Give a definition (including the domain) of the composite that exists, and explain why the other composite does not exist.

[3]

(b)

Find $f^{- 1} (x)$ and state the domain of $f^{- 1} .$

[3]