- The function f is defined by
$$f : x \mapsto \frac { 3 x - 5 } { x + 1 } , \quad x \in \mathbb { R } , \quad x \neq - 1$$
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
- Show that
$$\mathrm { ff } ( x ) = \frac { x + a } { x - 1 } , \quad x \in \mathbb { R } , \quad x \neq \pm 1$$
where \(a\) is an integer to be found.
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 \(\mathrm { fg } ( 2 )\).
- Find the range of g.
- Explain why the function \(g\) does not have an inverse.