| Date | May 2017 | Marks available | 3 | Reference code | 17M.1.sl.TZ1.2 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Let \(f(x) = 5x\) and \(g(x) = {x^2} + 1\), for \(x \in \mathbb{R}\).
Find \({f^{ - 1}}(x)\).
[2]
a.
Find \((f \circ g)(7)\).
[3]
b.
Markscheme
interchanging \(x\) and \(x\) (M1)
eg\(\,\,\,\,\,\)\(x = 5y\)
\({f^{ - 1}}\left( x \right) = \frac{x}{5}\) A1 N2
[2 marks]
a.
METHOD 1
attempt to substitute 7 into \(g(x)\) or \(f(x)\) (M1)
eg\(\,\,\,\,\,\)\({7^2} + 1,{\text{ }}5 \times 7\)
\(g(7) = 50\) (A1)
\(f\left( {50} \right) = 250\) A1 N2
METHOD 2
attempt to form composite function (in any order) (M1)
eg\(\,\,\,\,\,\)\(5({x^2} + 1),{\text{ }}{(5x)^2} + 1\)
correct substitution (A1)
eg\(\,\,\,\,\,\)\(5 \times ({7^2} + 1)\)
\((f \circ g)(7) = 250\) A1 N2
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
