5 A function is defined by \(\mathrm { f } ( x ) = \sinh ^ { - 1 } x + \sinh ^ { - 1 } \left( \frac { 1 } { x } \right)\), for \(x \neq 0\).
- When \(x > 0\), show that the value of \(\mathrm { f } ( x )\) for which \(\mathrm { f } ^ { \prime } ( x ) = 0\) is \(2 \ln ( 1 + \sqrt { 2 } )\).
\includegraphics[max width=\textwidth, alt={}, center]{72a1330a-c6dc-4f3a-9b0e-333b099f4509-3_497_659_520_708}
The diagram shows the graph of \(y = \mathrm { f } ( x )\) for \(x > 0\). Sketch the graph of \(y = \mathrm { f } ( x )\) for \(x < 0\) and state the range of values that \(\mathrm { f } ( x )\) can take for \(x \neq 0\).