OCR C3 — Question 5

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

5. The functions \(f\) and \(g\) are defined by $$\begin{aligned} & \mathrm { f } ( x ) \equiv x ^ { 2 } - 3 x + 7 , \quad x \in \mathbb { R } ,
& \mathrm {~g} ( x ) \equiv 2 x - 1 , \quad x \in \mathbb { R } . \end{aligned}$$
  1. Find the range of f .
  2. Evaluate \(g f ( - 1 )\).
  3. Solve the equation $$\operatorname { fg } ( x ) = 17$$