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The diagram shows the graph of \(y = \mathrm { f } ( x )\).
- On this diagram sketch the graph of \(y = \mathrm { f } ^ { - 1 } ( x )\).
It is now given that \(\mathrm { f } ( x ) = - \frac { x } { \sqrt { 4 - x ^ { 2 } } }\) where \(- 2 < x < 2\).
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
The function g is defined by \(\mathrm { g } ( x ) = 2 x\) for \(- a < x < a\), where \(a\) is a constant. - State the maximum possible value of \(a\) for which fg can be formed.
- Assuming that fg can be formed, find and simplify an expression for \(\mathrm { fg } ( x )\).