OCR C3 — Question 6

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
TopicComposite & Inverse Functions

6. The functions \(f\) and \(g\) are defined by $$\begin{aligned} & \mathrm { f } : x \rightarrow 3 x - 4 , \quad x \in \mathbb { R } ,
& \mathrm {~g} : x \rightarrow \frac { 2 } { x + 3 } , \quad x \in \mathbb { R } , \quad x \neq - 3 \end{aligned}$$
  1. Evaluate fg(1).
  2. Solve the equation \(\operatorname { gf } ( x ) = 6\).
  3. Find an expression for \(\mathrm { g } ^ { - 1 } ( x )\).