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 \(x \in S\).

Review question
# What are the greatest and least values of $f(x) - g(x)$ on this interval?

Ref: R9056

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

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 \(x \in S\).