2023 May TZ2 P1 Q6

The functions \(f\) and \(g\) are defined for \(x \in \mathbb{R}\) by

\(f(x) = ax+b\), where \(a, b \in \mathbb{Z}\)
\(g(x) = x^2 + x + 3\)

Find the two possible functions \(f\) such that \((g \circ f)(x) = 4x^2 -14x + 15\).[7]