| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Standard +0.3 This is a slightly easier than average C3 question. Part (a) is algebraic manipulation to simplify a rational expression (routine but requires care with factoring). Part (b) finding the inverse of f(x)=2/(x-1) is straightforward. Part (c) solving fg(x)=1/4 requires composition then solving a quadratic—all standard techniques with no novel insight required. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence1.02y Partial fractions: decompose rational functions |
3. The function $f$ is defined by
$$f : x \mapsto \frac { 5 x + 1 } { x ^ { 2 } + x - 2 } - \frac { 3 } { x + 2 } , x > 1$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathrm { f } ( x ) = \frac { 2 } { x - 1 } , x > 1$.
\item Find $\mathrm { f } ^ { - 1 } ( x )$.
The function g is defined by
$$\mathrm { g } : x \mapsto x ^ { 2 } + 5 , \quad x \in \mathbb { R } .$$
(b) Solve $\mathrm { fg } ( x ) = \frac { 1 } { 4 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q3 [12]}}