OCR C3 — Question 2

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

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