The function $f$ is given by $f(x) = \frac{48}{x - 1}$ for $3 \leq x \leq 7$. The function $g$ is given by $g(x) = 2x - 4$ for $a \leq x \leq b$, where $a$ and $b$ are constants.
(i)[2]
Find the greatest value of $a$ and the least value of $b$ that allow the composite function $gf$ to be formed.
(ii)[1]
It is now stated that the conditions needed to form $gf$ are satisfied. Find an expression for $gf(x)$.
(iii)[2]
Find an expression for $(gf)^{-1}(x)$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Greatest value $a=8$” …