The functions $f$ and $g$ are given by $f : x \mapsto 2x + 3$ for $x \leq 0$, and $g : x \mapsto x^2 - 6x$ for $x \leq 3$.
(i)[3]
Express $f^{-1}(x)$ using $x$, and solve the equation $f(x) = f^{-1}(x)$.
(ii)[3]
On one set of axes, sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, and show the coordinates of the point where they intersect together with how the graphs are related.
(iii)[5]
Find the set of values of $x$ for which $gf(x) \leq 16$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find the inverse function, $f^{-1}(x)=\frac12x-\frac32$” …