The functions $f$ and $g$ are specified below, with $a$ and $b$ taken as constants. $f(x) = 1 + \frac{2a}{x - a}$ for $x > a$ and $g(x) = bx - 2$ for $x \in \mathbb{R}$.
(a)[4]
Using the facts that $f(7) = \frac{5}{2}$ and $gf(5) = 4$, determine the values of $a$ and $b$.
(b)[1]
For the remainder of the question, use the value of $a$ that you found in (a).
Find the domain of $f^{-1}$.
(c)[3]
Find a formula for $f^{-1}(x)$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=7$ into the expression and solve for $a$” …