7. The function f is defined by
$$\mathrm { f } : x \mapsto \frac { 3 x - 5 } { x + 1 } , \quad x \in \mathbb { R } , x \neq - 1$$
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\)
- Show that
$$\operatorname { ff } ( x ) = \frac { x + a } { x - 1 } , \quad x \in \mathbb { R } , x \neq - 1 , x \neq 1$$
where \(a\) is an integer to be determined.
The function \(g\) is defined by
$$\mathrm { g } : x \mapsto x ^ { 2 } - 3 x , \quad x \in \mathbb { R } , 0 \leqslant x \leqslant 5$$
- Find the value of fg(2)
- Find the range of g