| Date | May 2016 | Marks available | 1 | Reference code | 16M.1.sl.TZ1.1 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Write down | Question number | 1 | Adapted from | N/A |
Question
Let \(f(x) = 8x + 3\) and \(g(x) = 4x\), for \(x \in \mathbb{R}\).
Write down \(g(2)\).
Find \((f \circ g)(x)\).
Find \({f^{ - 1}}(x)\).
Markscheme
\(g(2) = 8\) A1 N1
[1 mark]
attempt to form composite (in any order) (M1)
eg\(\,\,\,\,\,\)\(f(4x),{\text{ }}4 \times (8x + 3)\)
\((f \circ g)(x) = 32x + 3\) A1 N2
[2 marks]
interchanging \(x\) and \(y\) (may be seen at any time) (M1)
eg\(\,\,\,\,\,\)\(x = 8y + 3\)
\({f^{ - 1}}(x) = \frac{{x - 3}}{8}\,\,\,\,\,\left( {{\text{accept }}\frac{{x - 3}}{8},{\text{ }}y = \frac{{x - 3}}{8}} \right)\) A1 N2
[2 marks]
Examiners report
This question was successfully answered by most candidates. The inverse notation was sometimes mistakenly interpreted as derivative or reciprocal.
This question was successfully answered by most candidates. The inverse notation was sometimes mistakenly interpreted as derivative or reciprocal.
This question was successfully answered by most candidates. The inverse notation was sometimes mistakenly interpreted as derivative or reciprocal.
