Edexcel C3 2013 June — Question 7

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2013
SessionJune
TopicComposite & Inverse Functions

7. The function \(f\) has domain \(- 2 \leqslant x \leqslant 6\) and is linear from \(( - 2,10 )\) to \(( 2,0 )\) and from \(( 2,0 )\) to (6, 4). A sketch of the graph of \(y = \mathrm { f } ( x )\) is shown in Figure 1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2e29d66c-c3c6-4e4b-acfb-c73c60604d93-09_906_965_367_566} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure}
  1. Write down the range of f .
  2. Find \(\mathrm { ff } ( 0 )\). The function \(g\) is defined by $$\mathrm { g } : x \rightarrow \frac { 4 + 3 x } { 5 - x } , \quad x \in \mathbb { R } , \quad x \neq 5$$
  3. Find \(\mathrm { g } ^ { - 1 } ( x )\)
  4. Solve the equation \(\operatorname { gf } ( x ) = 16\)