9709 P11 - Jun 2020 - Q6
679
Functions f and g are defined for \(x \in \mathbb{R}\) by
\(f : x \mapsto \frac{1}{2}x - a\),
\(g : x \mapsto 3x + b\),
where \(a\) and \(b\) are constants.
(a) Given that \(gg(2) = 10\) and \(f^{-1}(2) = 14\), find the values of \(a\) and \(b\).
(b) Using these values of \(a\) and \(b\), find an expression for \(gf(x)\) in the form \(cx + d\), where \(c\) and \(d\) are constants.
