17M.1.AHL.TZ2.H_2

pestleMathematicsAIHLPaper 117M· sl-2-2-functions-notation-domain-range-and-inverse-as-reflectionsource ↗

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]

Find an expression for ${f^{ - 1}}(x)$ .

[2]

Write down the domain and range of ${f^{ - 1}}$ .

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$- 11 \leqslant f(x) \leqslant 21$ A1A1

Note: A1 for correct end points, A1 for correct inequalities.

[2 marks]

${f^{ - 1}}(x) = \sqrt[3]{{\frac{{x - 5}}{2}}}$ (M1)A1

[2 marks]

$- 11 \leqslant x \leqslant 21,{\text{ }} - 2 \leqslant {f^{ - 1}}(x) \leqslant 2$ A1A1

[2 marks]

Examiners’ report

[N/A]