9 The function f is defined by \(\mathrm { f } : x \mapsto \frac { 2 } { 3 - 2 x }\) for \(x \in \mathbb { R } , x \neq \frac { 3 } { 2 }\).
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
The function g is defined by \(\mathrm { g } : x \mapsto 4 x + a\) for \(x \in \mathbb { R }\), where \(a\) is a constant. - Find the value of \(a\) for which \(\operatorname { gf } ( - 1 ) = 3\).
- Find the possible values of \(a\) given that the equation \(\mathrm { f } ^ { - 1 } ( x ) = \mathrm { g } ^ { - 1 } ( x )\) has two equal roots.