The function f is given by $f(x)=\frac{4}{(3x-6)^2}+\frac{1}{(3x-6)^3}$ for $x>2$. The function g is given by $g(x)=4x-3$ when $x>a$.
(a)[4]
Find an expression for $f'(x)$ and hence decide whether f is an increasing function, a decreasing function or neither.
(b)[1]
State whether $f^{-1}$ exists. Give a reason for your answer.
(c)[1]
Find the range of g in terms of the constant $a$.
(d)[2]
Find the set of values of $a$ for which the composite function fg exists.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate the first term accurately: $\frac{4\times3\times(-2)}{(3x-6)^3}$” …