- The function \(f\) is defined by
$$\mathrm { f } : x \mapsto \frac { 3 - 2 x } { x - 5 } , \quad x \in \mathbb { R } , x \neq 5$$
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
(3)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3ff6824f-9fbf-4b5b-8bab-91332c549b36-10_901_1091_593_429}
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\caption{Figure 2}
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The function g has domain \(- 1 \leqslant x \leqslant 8\), and is linear from \(( - 1 , - 9 )\) to \(( 2,0 )\) and from \(( 2,0 )\) to \(( 8,4 )\). Figure 2 shows a sketch of the graph of \(y = \mathrm { g } ( x )\). - Write down the range of g.
- Find \(\operatorname { gg } ( 2 )\).
- Find \(\mathrm { fg } ( 8 )\).
- On separate diagrams, sketch the graph with equation
- \(y = | \mathrm { g } ( x ) |\),
- \(y = \mathrm { g } ^ { - 1 } ( x )\).
Show on each sketch the coordinates of each point at which the graph meets or cuts the axes.
- State the domain of the inverse function \(\mathrm { g } ^ { - 1 }\).