4. The functions f and g are defined for all real values of \(x\) by \(\mathrm { f } ( x ) = 2 x ^ { 2 } + 6 x\) and \(\mathrm { g } ( x ) = 3 x + 2\).
- Find the range of f.
- Give a reason why f has no inverse.
- Given that \(\mathrm { fg } ( - 2 ) = \mathrm { g } ^ { - 1 } ( a )\), where \(a\) is a constant, determine the value of \(a\).
- Determine the set of values of \(x\) for which \(\mathrm { f } ( x ) > \mathrm { g } ( x )\). Give your answer in set notation.
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\section*{5. In this question you must show detailed reasoning}
Find the equation of the normal to the curve \(y = \frac { x ^ { 2 } - 32 } { \sqrt { x } }\) at the point on the curve where \(x = 4\). Give your answer in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
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