Question 6 - A-Level Maths

Exam Board	Edexcel
Module	C3 (Core Mathematics 3)
Topic	Composite & Inverse Functions

The function f is defined by \(\mathrm { f } : x \rightarrow \frac { 3 x - 1 } { x - 3 } , x \in j , x \neq 3\).
1. Prove that \(\mathrm { f } ^ { - 1 } ( x ) = \mathrm { f } ( x )\) for all \(x \in j , x \neq 3\).
2. Hence find, in terms of \(k , \operatorname { ff } ( k )\), where \(x \neq 3\).
\begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{909b52e5-2f16-4eab-b691-9d8fcf9bcfd9-5_864_1205_605_242}
\end{figure} Figure 3 shows a sketch of the one-one function g , defined over the domain \(- 2 \leq x \leq 2\).
Find the value of \(\mathrm { fg } ( - 2 )\).
Sketch the graph of the inverse function \(\mathrm { g } ^ { - 1 }\) and state its domain. The function h is defined by \(\mathrm { h } : x \mapsto 2 \mathrm {~g} ( x - 1 )\).
Sketch the graph of the function h and state its range.