8 The functions f and g are defined for all real values of \(x\) by
$$\mathrm { f } ( x ) = x ^ { 2 } + 4 a x + a ^ { 2 } \text { and } \mathrm { g } ( x ) = 4 x - 2 a ,$$
where \(a\) is a positive constant.
- Find the range of f in terms of \(a\).
- Given that \(\mathrm { fg } ( 3 ) = 69\), find the value of \(a\) and hence find the value of \(x\) such that \(\mathrm { g } ^ { - 1 } ( x ) = x\).