| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Solve equation involving composites |
| Difficulty | Moderate -0.3 This is a slightly below-average C3 question. Part (a) is routine algebraic manipulation with common denominators. Part (b) requires understanding that 1/(x-1)(x+1) decreases from 1/2 toward 0 as x increases from 1, which is straightforward. Part (c) involves function composition and solving a quadratic, all standard techniques with no novel insight required. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02v Inverse and composite functions: graphs and conditions for existence |
The function f is given by
$$f : x \alpha \frac{x}{x^2-1} - \frac{1}{x+1}, \quad x > 1.$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\text{f}(x) = \frac{1}{(x-1)(x+1)}$. [3]
\item Find the range of f. [2]
\end{enumerate}
The function g is given by
$$g : x \alpha \frac{2}{x}, \quad x > 0.$$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Solve gf(x) = 70. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q1 [9]}}