| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Standard +0.0 This is a standard C3 question testing routine logarithm and differentiation techniques: evaluating a logarithmic function, finding a tangent (requiring the chain rule), and finding an inverse function. All parts are textbook exercises with no novel problem-solving required, making this exactly average difficulty for A-level maths. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.06d Natural logarithm: ln(x) function and properties1.07m Tangents and normals: gradient and equations |
The function f is defined by
$$\text{f}(x) \equiv 2 + \ln (3x - 2), \quad x \in \mathbb{R}, \quad x > \frac{2}{3}.$$
\begin{enumerate}[label=(\roman*)]
\item Find the exact value of $\text{f}(1)$. [2]
\item Find an equation for the tangent to the curve $y = \text{f}(x)$ at the point where $x = 1$. [4]
\item Find an expression for $\text{f}^{-1}(x)$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q5 [8]}}