5. The functions \(f\) and \(g\) are defined by $$\begin{aligned} & \mathrm { f } : x \alpha \quad | x - a | + a , x \in \mathbb { R }
& \mathrm {~g} : x \alpha \quad 4 x + a , \quad x \in \mathbb { R } \end{aligned}$$ where \(a\) is a positive constant.

1. On the same diagram, sketch the graphs of f and g , showing clearly the coordinates of any points at which your graphs meet the axes.
2. Use algebra to find, in terms of \(a\), the coordinates of the point at which the graphs of f and g intersect.
3. Find an expression for \(\mathrm { fg } ( x )\).
4. Solve, for \(x\) in terms of \(a\), the equation $$\mathrm { fg } ( x ) = 3 a$$ \section*{6.}