Edexcel P3 2022 October — Question 2

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2022
SessionOctober
TopicComposite & Inverse Functions

2. The functions f and g are defined by $$\begin{array} { l l } f ( x ) = 5 - \frac { 4 } { 3 x + 2 } & x \geqslant 0
g ( x ) = \left| 4 \sin \left( \frac { x } { 3 } + \frac { \pi } { 6 } \right) \right| & x \in \mathbb { R } \end{array}$$
  1. Find the range of f
    1. Find \(\mathrm { f } ^ { - 1 } ( x )\)
    2. Write down the domain of \(\mathrm { f } ^ { - 1 }\)
  2. Find \(\mathrm { fg } ( - \pi )\)