Edexcel Paper 2 Specimen — Question 4

Exam BoardEdexcel
ModulePaper 2 (Paper 2)
SessionSpecimen
TopicComposite & Inverse Functions

4. Given $$\begin{aligned} & \mathrm { f } ( x ) = \mathrm { e } ^ { x } , \quad x \in \mathbb { R }
& \mathrm {~g} ( x ) = 3 \ln x , \quad x > 0 , x \in \mathbb { R } \end{aligned}$$
  1. find an expression for \(\mathrm { gf } ( x )\), simplifying your answer.
  2. Show that there is only one real value of \(x\) for which \(\operatorname { gf } ( x ) = \operatorname { fg } ( x )\)