The functions $f$ and $g$ are given by
$f(x) = \frac{2x + 1}{2x - 1}$ for $x \neq \frac{1}{2}$,
$g(x) = x^2 + 4$ for $x \in \mathbb{R}$.
The diagram shows a section of the graph of $y = f(x)$.
(a)[1]
Give the domain of $f^{-1}$.
(b)[3]
Find an algebraic expression for $f^{-1}(x)$.
(c)[2]
Find $gf^{-1}(3)$.
(d)[1]
Explain why $g^{-1}(x)$ cannot be defined.
(e)[6]
Show that $1 + \frac{2}{2x - 1}$ may be rewritten as $\frac{2x + 1}{2x - 1}$. Hence find the area of the triangle enclosed by the tangent to the curve $y = f(x)$ at the point where $x = 1$ and the $x$- and $y$-axes.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly gives the domain as $x\neq\pm1$.” …