OCR C3 2009 June — Question 5

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2009
SessionJune
TopicComposite & Inverse Functions

5 The functions f and g are defined for all real values of \(x\) by $$\mathrm { f } ( x ) = 3 x - 2 \quad \text { and } \quad \mathrm { g } ( x ) = 3 x + 7$$ Find the exact coordinates of the point at which
  1. the graph of \(y = \operatorname { fg } ( x )\) meets the \(x\)-axis,
  2. the graph of \(y = \mathrm { g } ( x )\) meets the graph of \(y = \mathrm { g } ^ { - 1 } ( x )\),
  3. the graph of \(y = | \mathrm { f } ( x ) |\) meets the graph of \(y = | \mathrm { g } ( x ) |\).