CAIE P1 2006 November — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2006
SessionNovember
TopicInequalities

10 The function f is defined by \(\mathrm { f } : x \mapsto x ^ { 2 } - 3 x\) for \(x \in \mathbb { R }\).
  1. Find the set of values of \(x\) for which \(\mathrm { f } ( x ) > 4\).
  2. Express \(\mathrm { f } ( x )\) in the form \(( x - a ) ^ { 2 } - b\), stating the values of \(a\) and \(b\).
  3. Write down the range of f .
  4. State, with a reason, whether f has an inverse. The function g is defined by \(\mathrm { g } : x \mapsto x - 3 \sqrt { } x\) for \(x \geqslant 0\).
  5. Solve the equation \(\mathrm { g } ( x ) = 10\).