5．The function f is defined on the domain \([ - 2,2 ]\) by： $$f ( x ) = \left\{ \begin{array} { r l r } - k x ( 2 + x ) & \text { if } & - 2 \leq x < 0 ,
k x ( 2 - x ) & \text { if } & 0 \leq x \leq 2 , \end{array} \right.$$ where \(k\) is a positive constant．
The function g is defined on the domain \([ - 2,2 ]\) by \(\mathrm { g } ( x ) = ( 2.5 ) ^ { 2 } - x ^ { 2 }\) ．
（a）Prove that there is a value of \(k\) such that the graph of f touches the graph of g ．
（b）For this value of \(k\) sketch the graphs of the functions f and g on the same axes，stating clearly where the graphs touch．
（c）Find the exact area of the region bounded by the two graphs．