| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find composite function expression |
| Difficulty | Easy -1.2 This is a straightforward composite and inverse function question requiring only routine algebraic manipulation. Finding the inverse of f(x)=2x is trivial, composing it with g involves simple substitution, and stating the range requires basic understanding of quadratic functions. All steps are standard textbook exercises with no problem-solving or novel insight required. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
2. The function $f$ is defined by
$$\mathrm { f } : x \mapsto 2 x , \quad x \in \mathbb { R }$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { f } ^ { - 1 } ( x )$ and state the domain of $\mathrm { f } ^ { - 1 }$.
The function g is defined by
$$\mathrm { g } : x \mapsto 3 x ^ { 2 } + 2 , \quad x \in \mathbb { R }$$
\item Find $\mathrm { gf } ^ { - 1 } ( x )$.
\item State the range of $\mathrm { gf } ^ { - 1 } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q2 [5]}}