Moderate -0.8 This is a straightforward inverse function question requiring only the standard technique of swapping x and y, then solving for y using logarithms. Finding the inverse of an exponential function and stating the domain (x > 0) is a routine textbook exercise with no problem-solving element, making it easier than average.
4 The function f is defined by \(\mathrm { f } ( x ) = \mathrm { e } ^ { x - 4 } , x \in \mathbb { R }\)
Find \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.
Takes logs of equation — must be correct use of logs
\(\ln y = x - 4\) leading to \(4 + \ln y = x\)
A1
Obtains correct inverse function in any correct form
\(f^{-1}(x) = 4 + \ln x,\ x > 0\)
B1
Deduces correct domain
Total: 3 marks
## Question 4:
| Working | Mark | Guidance |
|---|---|---|
| $y = e^{x-4}$ | M1 | Takes logs of equation — must be correct use of logs |
| $\ln y = x - 4$ leading to $4 + \ln y = x$ | A1 | Obtains correct inverse function in any correct form |
| $f^{-1}(x) = 4 + \ln x,\ x > 0$ | B1 | Deduces correct domain |
**Total: 3 marks**
4 The function f is defined by $\mathrm { f } ( x ) = \mathrm { e } ^ { x - 4 } , x \in \mathbb { R }$\\
Find $\mathrm { f } ^ { - 1 } ( x )$ and state its domain.\\
\hfill \mbox{\textit{AQA Paper 1 2018 Q4 [3]}}