4 The function f is defined by \(\mathrm { f } ( x ) = \frac { 48 } { x - 1 }\) for \(3 \leqslant x \leqslant 7\). The function g is defined by \(\mathrm { g } ( x ) = 2 x - 4\) for \(a \leqslant x \leqslant b\), where \(a\) and \(b\) are constants.
- Find the greatest value of \(a\) and the least value of \(b\) which will permit the formation of the composite function gf.
It is now given that the conditions for the formation of gf are satisfied. - Find an expression for \(\operatorname { gf } ( x )\).
- Find an expression for \(( \mathrm { gf } ) ^ { - 1 } ( x )\).