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.
- 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 \(\operatorname { gf } ( - 2 ) = - 12\)
- find the possible values of \(k\).