Edexcel P3 2024 June — Question 5

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2024
SessionJune
TopicComposite & Inverse Functions

  1. The functions \(f\) and \(g\) are defined by
$$\begin{aligned} & \mathrm { f } ( x ) = 2 + 5 \ln x \quad x > 0
& \mathrm {~g} ( x ) = \frac { 6 x - 2 } { 2 x + 1 } \quad x > \frac { 1 } { 3 } \end{aligned}$$
  1. Find \(\mathrm { f } ^ { - 1 } ( 22 )\)
  2. Use differentiation to prove that g is an increasing function.
  3. Find \(\mathrm { g } ^ { - 1 }\)
  4. Find the range of fg