| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Solve equation involving composites |
| Difficulty | Standard +0.3 This is a slightly above-average C3 question. Part (a) requires algebraic manipulation with partial fractions in reverse, which is routine but requires care. Part (b) involves finding the range using calculus or analysis of the simplified form. Part (c) combines composite functions with equation solving. All techniques are standard C3 material with no novel insights required, making it moderately straightforward but with enough steps to be slightly above typical difficulty. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02u Functions: definition and vocabulary (domain, range, mapping) |
The function $f$ is given by
$$f : x \mapsto \frac{x}{x^2 - 1} - \frac{1}{x + 1}, \quad x > 1.$$
\begin{enumerate}[label=(\alph*)]
\item Show that $f(x) = \frac{1}{(x-1)(x+1)}$. [3]
\item Find the range of $f$. [2]
\end{enumerate}
The function $g$ is given by
$$g : x \mapsto \frac{2}{x}, \quad x > 0.$$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Solve $gf(x) = 70$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q5 [9]}}