Edexcel P3 2021 October — Question 1

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2021
SessionOctober
TopicPartial Fractions
TypeFind inverse function after simplification

  1. The function f is defined by
$$\mathrm { f } ( x ) = \frac { 5 x } { x ^ { 2 } + 7 x + 12 } + \frac { 5 x } { x + 4 } \quad x > 0$$
  1. Show that \(\mathrm { f } ( x ) = \frac { 5 x } { x + 3 }\)
  2. Find \(\mathrm { f } ^ { - 1 }\)
    1. Find, in simplest form, \(\mathrm { f } ^ { \prime } ( x )\).
    2. Hence, state whether f is an increasing or a decreasing function, giving a reason for your answer.
      (3)