19M.2.AHL.TZ1.H_4

pestleMathematicsAAHLPaper 219M· sl-2-2-functions-notation-domain-range-and-inverse-as-reflectionsource ↗

The function $f$ is defined by $f\left( x \right) = {\text{sec}}\,x + 2$ , $0 \leqslant x < \frac{\pi }{2}$ .

Write down the range of $f$ .

[1]

Find $f'\left( x \right)$ , stating its domain.

[4]

Markscheme / solution

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

$f\left( x \right)$ ≥ 3 A1

[1 mark]

$x = {\text{sec}}\,y + 2$ (M1)

Note: Exchange of variables can take place at any point.

${\text{cos}}\,y = \frac{1}{{x - 2}}$ (A1)

$f'\left( x \right) = {\text{arccos}}\left( {\frac{1}{{x - 2}}} \right)$ , $x$ ≥ 3 A1A1

Note: Allow follow through from (a) for last A1 mark which is independent of earlier marks in (b).

[4 marks]

Examiners’ report

[N/A]