Find the area of triangle \(A B C\), giving your answer correct to 1 decimal place.
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The diagram shows the graph of \(y = \mathrm { f } ^ { - 1 } ( x )\), where \(\mathrm { f } ^ { - 1 }\) is defined by \(\mathrm { f } ^ { - 1 } ( x ) = \frac { 1 - 5 x } { 2 x }\) for \(0 < x \leqslant 2\).
Find an expression for \(\mathrm { f } ( x )\) and state the domain of f .
The function g is defined by \(\mathrm { g } ( x ) = \frac { 1 } { x }\) for \(x \geqslant 1\). Find an expression for \(\mathrm { f } ^ { - 1 } \mathrm {~g} ( x )\), giving your answer in the form \(a x + b\), where \(a\) and \(b\) are constants to be found.