CAIE A-Level Mathematics AS 1.2.4 One One and Inverse Functions Questions

Practise inverse functions, restrictions and graph relationships within the AS mathematics syllabus.

Exam points

determine inverse functions algebraically
state domain restrictions for inverses
relate inverse graphs to the line y=x

[Maximum number: 2]

Figure for Question CAIE A-Level Mathematics AS 1.2.4 One One and Inverse Functions Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the graph of y=f(x) where the function f is defined by

f(x)=3+2 \sin \frac{1}{4} x \text { for } 0 \leqslant x \leqslant 2 \pi .

On the diagram above, sketch the graph of $y=\mathrm{f}^{-1}(x)$ .

*B1

The line y=x correctly drawn. Can be implied by
reasonably correct graph of $\mathrm{f}^{-1}(x)$ .

DB1

Fully correct (needs to reach $y=2 \pi$ and x-axis and cross
the line y=x in the correct squares).

Answer diagram

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CAIE A-Level Mathematics AS 1.2.4 One One and Inverse Functions Questions question 1