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

Practise sketching an inverse by reflecting a one-to-one graph in y = x and transferring intercepts, endpoints, asymptotes and curve shape to exchanged coordinates.

Exam points

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

[Maximum number: 3]

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 function f is defined by $\mathrm{f}(x)=\frac{2}{x^{2}}+4$ for x<0. The diagram shows the graph of y=f(x).

(a)

On this diagram, sketch the graph of $y=\mathrm{f}^{-1}(x)$ . Show any relevant mirror line.

[ 2 ]

(b)

Explain why the equation $\mathrm{f}^{-1}(x)=\mathrm{f}(x)$ has no solution.

[ 1 ]

Because $\mathrm{f}^{-1}$ is always negative and f is always positive or curves do not
intersect
Marking guidance:

Accept other correct answers e.g. ' f is only defined for
positive values of x and $\mathrm{f}^{-1}$ is only defined for negative
values of x ' or 'domains do not overlap' or 'the y values
cannot be the same' or 'the x values cannot be the same'.

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

Question (a)

Question (b)