9 The functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } ( x ) = x ^ { 2 } - 4 x + 3 \text { for } x > c , \text { where } c \text { is a constant, }
& \mathrm { g } ( x ) = \frac { 1 } { x + 1 } \quad \text { for } x > - 1
\end{aligned}$$
- Express \(\mathrm { f } ( x )\) in the form \(( x - a ) ^ { 2 } + b\).
It is given that f is a one-one function. - State the smallest possible value of \(c\).
It is now given that \(c = 5\). - Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).
- Find an expression for \(\mathrm { gf } ( x )\) and state the range of gf .