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.

Note that \(\mathbb{R}\) means the set of real numbers, and in set theory “\(x\in S\)” means “\(x\) is a member of the set \(S\)”. So here \(x\in \mathbb{R}\) tells us that \(x\) is a real number.