- The function f is defined by
$$f ( x ) = \frac { 8 x + 5 } { 2 x + 3 } \quad x > - \frac { 3 } { 2 }$$
- Find \(\mathrm { f } ^ { - 1 } \left( \frac { 3 } { 2 } \right)\)
- Show that
$$\mathrm { f } ( x ) = A + \frac { B } { 2 x + 3 }$$
where \(A\) and \(B\) are constants to be found.
The function \(g\) is defined by
$$g ( x ) = 16 - x ^ { 2 } \quad 0 \leqslant x \leqslant 4$$
- State the range of \(\mathrm { g } ^ { - 1 }\)
- Find the range of \(\mathrm { fg } ^ { - 1 }\)