where \(x\in \mathbb{R}\) in each case.

Find the solution set, \(S\), of the inequality \(f(x)\ge g(x)\).

Sketch the graph of \(y=f(x)-g(x)\) for \(x\in S\), and state the greatest and least values of \(f(x)-g(x)\) for \(x\in S\).

Functions \(f\) and \(g\) are defined by
\[\begin{align*}
f&:x\mapsto x(x-1), \\
g&:x\mapsto (x-1)(3x-5),
\end{align*}\]

where \(x\in \mathbb{R}\) in each case.

Find the solution set, \(S\), of the inequality \(f(x)\ge g(x)\).

Sketch the graph of \(y=f(x)-g(x)\) for \(x\in S\), and state the greatest and least values of \(f(x)-g(x)\) for \(x\in S\).