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