The functions $f$ and $g$ are specified by $f : x \mapsto 3x - 4$, $x \in \mathbb{R}$, and $g : x \mapsto 2(x - 1)^3 + 8$, $x > 1$.
(i)[2]
Evaluate the value of $fg(2)$.
(ii)[3]
On a single diagram, sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, and show clearly how the two graphs are related.
(iii)[3]
Find an expression for $g'(x)$ and use your result to explain why $g$ has an inverse.
(iv)[4]
Express both $f^{-1}(x)$ and $g^{-1}(x)$ as functions of $x$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the inverse first, then calculate $g(2)=f(10)=26$.” …