4. The function f is defined by
$$\mathrm { f } ( x ) \equiv x ^ { 2 } - 2 a x , \quad x \in \mathbb { R }$$
where \(a\) is a positive constant.
- Showing the coordinates of any points where the graph meets the axes, sketch the graph of \(y = | \mathrm { f } ( x ) |\).
The function \(g\) is defined by
$$\mathrm { g } ( x ) \equiv 3 a x , \quad x \in \mathbb { R } .$$
- Find \(\mathrm { fg } ( \mathrm { a } )\) in terms of \(a\).
- Solve the equation
$$\operatorname { gf } ( x ) = 9 a ^ { 3 }$$