Edexcel C3 2013 June — Question 6

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2013
SessionJune
TopicFunction Transformations
TypeComposite transformation sketch

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0f6fd881-4d4b-4f80-96cc-6da41cc33c60-10_775_1392_233_278} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of the graph of \(y = \mathrm { f } ( x )\) where $$\mathrm { f } ( x ) = \left\{ \begin{array} { r r } 5 - 2 x , & x \leqslant 4
\mathrm { e } ^ { 2 x - 8 } - 4 , & x > 4 \end{array} \right.$$
  1. State the range of \(\mathrm { f } ( x )\).
  2. Determine the exact value of ff(0).
  3. Solve \(\mathrm { f } ( x ) = 21\) Give each answer as an exact answer.
  4. Explain why the function f does not have an inverse.