Edexcel P3 2021 June — Question 4

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2021
SessionJune
TopicComposite & Inverse Functions

4. The functions f and g are defined by $$\begin{array} { l l } \mathrm { f } ( x ) = \frac { 4 x + 6 } { x - 5 } & x \in \mathbb { R } , x \neq 5
\mathrm {~g} ( x ) = 5 - 2 x ^ { 2 } & x \in \mathbb { R } , x \leqslant 0 \end{array}$$
  1. Solve the equation $$\operatorname { fg } ( x ) = 3$$
  2. Find \(\mathrm { f } ^ { - 1 }\)
  3. Sketch and label, on the same axes, the curve with equation \(y = \mathrm { g } ( x )\) and the curve with equation \(y = \mathrm { g } ^ { - 1 } ( x )\). Show on your sketch the coordinates of the points where each curve meets or cuts the coordinate axes.