9709 P13 - Jun 2013 - Q10
720
The function f is defined by \(f : x \mapsto 2x + k, \ x \in \mathbb{R}\), where \(k\) is a constant.
(i) In the case where \(k = 3\), solve the equation \(ff(x) = 25\).
The function g is defined by \(g : x \mapsto x^2 - 6x + 8, \ x \in \mathbb{R}\).
(ii) Find the set of values of \(k\) for which the equation \(f(x) = g(x)\) has no real solutions.
The function h is defined by \(h : x \mapsto x^2 - 6x + 8, \ x > 3\).
(iii) Find an expression for \(h^{-1}(x)\).
