Edexcel P3 2023 June — Question 6

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2023
SessionJune
TopicModulus function

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bef290fb-fbac-4c9c-981e-5e323ac7182e-14_752_794_251_639} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of the graph \(y = \mathrm { f } ( x )\), where $$f ( x ) = 3 | x - 2 | - 10$$ The vertex of the graph is at point \(P\), shown in Figure 2.
  1. Find the coordinates of \(P\)
  2. Find \(\mathrm { ff } ( 0 )\)
  3. Solve the inequality $$3 | x - 2 | - 10 < 5 x + 10$$
  4. Solve the equation $$\mathrm { f } ( | x | ) = 0$$