Edexcel C3 — Question 7

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
TopicPartial Fractions
TypeFind inverse function after simplification

7. $$f ( x ) = 1 + \frac { 4 x } { 2 x - 5 } - \frac { 15 } { 2 x ^ { 2 } - 7 x + 5 } , \quad x \in \mathbb { R } , \quad x < 1$$
  1. Show that $$f ( x ) = \frac { 3 x + 2 } { x - 1 }$$
  2. Find an expression for the inverse function \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.
  3. Solve the equation \(\mathrm { f } ( x ) = 2\).