| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Difficulty | Standard +0.8 This AEA question involves finding an inverse function and differentiating a logarithm with quotient rule, then simplifying. Part (a) is routine (swap and rearrange), but part (b) requires careful application of chain rule with quotient rule and algebraic manipulation to simplify the result. The AEA context and need for clean simplification elevates this slightly above standard A-level, though it remains accessible with solid technique. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.07l Derivative of ln(x): and related functions |
The function f is given by
$$f(x) = \ln(2x - 5), \quad x > 2.5$$
(a) Find $f^{-1}(x)$.
[2]
The function g has domain $x > 2$ and
$$g(x) = \ln\left(\frac{x + 10}{x - 2}\right), \quad x > 2$$
(b) Find $g(x)$ and simplify your answer.
[3]
\hfill \mbox{\textit{Edexcel AEA 2014 Q1 [5]}}