| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.hl.TZ2.2 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The function \(f\) is defined by \(f(x) = 2{x^3} + 5,{\text{ }} - 2 \leqslant x \leqslant 2\).
Write down the range of \(f\).
[2]
a.
Find an expression for \({f^{ - 1}}(x)\).
[2]
b.
Write down the domain and range of \({f^{ - 1}}\).
[2]
c.
Markscheme
\( - 11 \leqslant f(x) \leqslant 21\) A1A1
Note: A1 for correct end points, A1 for correct inequalities.
[2 marks]
a.
\({f^{ - 1}}(x) = \sqrt[3]{{\frac{{x - 5}}{2}}}\) (M1)A1
[2 marks]
b.
\( - 11 \leqslant x \leqslant 21,{\text{ }} - 2 \leqslant {f^{ - 1}}(x) \leqslant 2\) A1A1
[2 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
