Edexcel C34 2019 January — Question 3

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2019
SessionJanuary
TopicComposite & Inverse Functions

3. The function f is defined by $$f : x \mapsto 2 x ^ { 2 } + 3 k x + k ^ { 2 } \quad x \in \mathbb { R } , - 4 k \leqslant x \leqslant 0$$ where \(k\) is a positive constant.
  1. Find, in terms of \(k\), the range of f . The function g is defined by $$\mathrm { g } : x \mapsto 2 k - 3 x \quad x \in \mathbb { R }$$ Given that \(\operatorname { gf } ( - 2 ) = - 12\)
  2. find the possible values of \(k\).