13 The function f is defined by
$$\mathrm { f } ( x ) = \frac { 2 x + 3 } { x - 2 } \quad x \in \mathbb { R } , x \neq 2$$
13
- Find f-1
13
- (ii) Write down an expression for \(\mathrm { ff } ( x )\).
13 - The function g is defined by
$$g ( x ) = \frac { 2 x ^ { 2 } - 5 x } { 2 } \quad x \in \mathbb { R } , 0 \leq x \leq 4$$
13
- Find the range of g .
13
- (ii) Determine whether g has an inverse.
Fully justify your answer. - Show that
$$g f ( x ) = \frac { 48 + 29 x - 2 x ^ { 2 } } { 2 x ^ { 2 } - 8 x + 8 }$$
13
- It can be shown that fg is given by
$$f g ( x ) = \frac { 4 x ^ { 2 } - 10 x + 6 } { 2 x ^ { 2 } - 5 x - 4 }$$
with domain \(\{ x \in \mathbb { R } : 0 \leq x \leq 4 , x \neq a \}\)
Find the value of \(a\).
Fully justify your answer.