7. 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 each graph meets the axes, sketch on separate diagrams the graphs of
- \(\quad y = | \mathrm { f } ( x ) |\),
- \(y = \mathrm { f } ( | x | )\).
The function g is defined by
$$\mathrm { g } ( x ) \equiv 3 a x , \quad x \in \mathbb { R } .$$
- Find fg(a) in terms of \(a\).
- Solve the equation
$$\operatorname { gf } ( x ) = 9 a ^ { 3 }$$