Edexcel C3 2017 June — Question 3

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2017
SessionJune
TopicComposite & Inverse Functions

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f0a633e3-5c63-4d21-8ffa-d4e7dc43a536-06_476_1107_221_422} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the graph of \(y = \mathrm { g } ( x )\), where $$g ( x ) = 3 + \sqrt { x + 2 } , \quad x \geqslant - 2$$
  1. State the range of g .
  2. Find \(\mathrm { g } ^ { - 1 } ( x )\) and state its domain.
  3. Find the exact value of \(x\) for which $$\mathrm { g } ( x ) = x$$
  4. Hence state the value of \(a\) for which $$\mathrm { g } ( a ) = \mathrm { g } ^ { - 1 } ( a )$$