The function f is defined for all real values of \(x\) by
$$f ( x ) = e ^ { 2 x } - 3 e ^ { - 2 x } .$$
(a) Show that \(\mathrm { f } ^ { \prime } ( x ) > 0\) for all \(x\).
(b) Show that the set of values of \(x\) for which \(\mathrm { f } ^ { \prime \prime } ( x ) > 0\) is the same as the set of values of \(x\) for which \(\mathrm { f } ( x ) > 0\), and state what this set of values is.
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The function g is defined for all real values of \(x\) by
$$\mathrm { g } ( x ) = \mathrm { e } ^ { 2 x } + k \mathrm { e } ^ { - 2 x } ,$$
where \(k\) is a constant greater than 1 . The graph of \(y = \mathrm { g } ( x )\) is shown above. Find the range of g , giving your answer in simplified form.