Edexcel P3 2022 June — Question 2

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

2. The functions f and g are defined by $$\begin{array} { l l } \mathrm { f } ( x ) = \frac { 5 - x } { 3 x + 2 } & x \in \mathbb { R } , x \neq - \frac { 2 } { 3 }
\mathrm {~g} ( x ) = 2 x - 7 & x \in \mathbb { R } \end{array}$$
  1. Find the value of \(\mathrm { fg } ( 5 )\)
  2. Find \(\mathrm { f } ^ { - 1 }\)
  3. Solve the equation $$\mathrm { f } \left( \frac { 1 } { a } \right) = \mathrm { g } ( a + 3 )$$