| Exam Board | Edexcel |
|---|---|
| Module | C34 (Core Mathematics 3 & 4) |
| Year | 2018 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Standard +0.2 This is a straightforward multi-part question testing standard C3/C4 techniques: finding inverse of exponential function (routine application of logarithms), evaluating a composite function (direct substitution), sketching absolute value graphs, and solving absolute value equations. All parts are textbook exercises requiring only procedural knowledge with no novel problem-solving or insight needed. Slightly easier than average due to the routine nature of each component. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
\begin{enumerate}
\item (i) The functions $f$ and $g$ are defined by
\end{enumerate}
$$\begin{array} { l l }
\mathrm { f } : x \rightarrow \mathrm { e } ^ { 2 x } - 5 , & x \in \mathbb { R } \\
\mathrm {~g} : x \rightarrow \ln ( 3 x - 1 ) , & x \in \mathbb { R } , x > \frac { 1 } { 3 }
\end{array}$$
(a) Find $\mathrm { f } ^ { - 1 }$ and state its domain.\\
(b) Find $\mathrm { fg } ( 3 )$, giving your answer in its simplest form.\\
(ii) (a) Sketch the graph with equation
$$y = | 4 x - a |$$
where $a$ is a positive constant. State the coordinates of each point where the graph cuts or meets the coordinate axes.
Given that
$$| 4 x - a | = 9 a$$
where $a$ is a positive constant,\\
(b) find the possible values of
$$| x - 6 a | + 3 | x |$$
giving your answers, in terms of $a$, in their simplest form.
\hfill \mbox{\textit{Edexcel C34 2018 Q5 [12]}}