The curve C has equation \(y = f(x)\), where \(f(x) = \frac{x^2}{x+1}\).

1. Find the equations of the asymptotes of C.
2. Find the coordinates of any stationary points on C.
3. Sketch C.
4. Find the coordinates of any stationary points on the curve with equation \(y = \frac{1}{f(x)}\).
5. Sketch the curve with equation \(y = \frac{1}{f(x)}\) and find, in exact form, the set of values for which \(\frac{1}{f(x)} > f(x)\).