9709 P11 - Jun 2021 - Q9
673
Functions f and g are defined as follows:
\(f(x) = (x - 2)^2 - 4\) for \(x \geq 2\),
\(g(x) = ax + 2\) for \(x \in \mathbb{R}\),
where \(a\) is a constant.
(a) State the range of \(f\).
(b) Find \(f^{-1}(x)\).
(c) Given that \(a = -\frac{5}{3}\), solve the equation \(f(x) = g(x)\).
(d) Given instead that \(gg f^{-1}(12) = 62\), find the possible values of \(a\).
