10. The function \(f\) has domain \([ 4 , \infty )\) and is defined by
$$f ( x ) = \frac { 2 ( 3 x + 1 ) } { x ^ { 2 } - 2 x - 3 } + \frac { x } { x + 1 }$$
- Show that \(f ( x ) = \frac { x + 2 } { x - 3 }\).
10. The function \(f\) has domain \([ 4 , \infty )\) and is defined by
$$f ( x ) = \frac { 2 ( 3 x + 1 ) } { x ^ { 2 } - 2 x - 3 } + \frac { x } { x + 1 } .$$ - Show that \(f ( x ) = \frac { x + 2 } { x - 3 }\). [4]
- Determine the range of \(f ( x )\).
- Find an expression for \(f ^ { - 1 } ( x )\) and write down the domain and range of \(f ^ { - 1 }\).
- Find the value of \(x\) when \(f ( x ) = f ^ { - 1 } ( x )\).