7 The curve \(C\) has equation \(y = f ( x )\), where \(f ( x ) = \frac { x ^ { 2 } } { x + 1 }\).
- Find the equations of the asymptotes of \(C\).
- Find the coordinates of any stationary points on \(C\).
- Sketch \(C\).
- Find the coordinates of any stationary points on the curve with equation \(\mathrm { y } = \frac { 1 } { \mathrm { f } ( \mathrm { x } ) }\).
- Sketch the curve with equation \(y = \frac { 1 } { f ( x ) }\) and find, in exact form, the set of values for which
$$\frac { 1 } { \mathrm { f } ( x ) } > \mathrm { f } ( x ) .$$
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