OCR C3 — Question 8

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
TopicModulus function

8. The functions f and g are defined for all real values of \(x\) by $$\begin{aligned} & \mathrm { f } : x \rightarrow | x - 3 a |
& \mathrm { g } : x \rightarrow | 2 x + a | \end{aligned}$$ where \(a\) is a positive constant.
  1. Evaluate fg(-2a).
  2. Sketch on the same diagram the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { g } ( x )\), showing the coordinates of any points where each graph meets the coordinate axes.
  3. Solve the equation $$\mathrm { f } ( x ) = \mathrm { g } ( x )$$