The function $f$ is specified by $f(x) = 2 - \dfrac{3}{4x - p}$, with domain $x > \dfrac{p}{4}$ and $p$ a constant.
(a)[3]
Find $f'(x)$ and then decide whether $f$ is an increasing function, a decreasing function or neither.
(b)[4]
Write $f^{-1}(x)$ as $\dfrac{p}{a} - \dfrac{b}{cx - d}$, with $a$, $b$, $c$ and $d$ all integers.
(c)[1]
Hence State the value of $p$ that satisfies $f^{-1}(x) = f(x)$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to obtain $f'(x)=\frac{12}{(4x-p)^2}$.” …