CAIE P1 2003 June — Question 11

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2003
SessionJune
TopicComposite & Inverse Functions

11 The equation of a curve is \(y = 8 x - x ^ { 2 }\).
  1. Express \(8 x - x ^ { 2 }\) in the form \(a - ( x + b ) ^ { 2 }\), stating the numerical values of \(a\) and \(b\).
  2. Hence, or otherwise, find the coordinates of the stationary point of the curve.
  3. Find the set of values of \(x\) for which \(y \geqslant - 20\). The function g is defined by \(\mathrm { g } : x \mapsto 8 x - x ^ { 2 }\), for \(x \geqslant 4\).
  4. State the domain and range of \(\mathrm { g } ^ { - 1 }\).
  5. Find an expression, in terms of \(x\), for \(\mathrm { g } ^ { - 1 } ( x )\).