6. For all real values of \(x\), the functions f and g are defined by \(\mathrm { f } ( x ) = x ^ { 2 } + 8 a x + 4 a ^ { 2 }\) and \(\mathrm { g } ( x ) = 6 x - 2 a\), where \(a\) is a positive constant.
- Find \(\mathrm { fg } ( x )\). Determine the range of \(\mathrm { fg } ( x )\) in terms of \(a\).
- If \(f g ( 2 ) = 144\), find the value of \(a\).
- Determine whether the function fg has an inverse.
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