IB Maths AA HL Sl 2 5 Composite and Inverse Functions Questions

Practise IB Maths AA HL 2.5 by analysing composite and inverse functions with domain restrictions and multiple possible mappings.

Exam points

Form and evaluate composite functions and inverse functions.
Determine domains, ranges and algebraic forms of composites and inverses using complete evidence.

[Maximum number: 5]

Consider the function $f(x)=a x^{3}+b x^{2}+c x+d$ , where $x \in \mathbb{R}$ and $a, b, c, d \in \mathbb{R}$ .

Sketch the graphs of y=g(x) and $y=g^{-1}(x)$ on the same set of axes, indicating the points where each graph crosses the coordinate axes.

Figure for Answer to Question IB Maths AA HL Sl 2 5 Composite and Inverse Functions Questions question 1 — IB Maths AA HL

Note: Award A1 for correct 'shape' of g (allow non-stationary point of inflexion)
Award A1 for each correct intercept of g
Award M1 for attempt to reflect their graph in y=x, A1 for completely correct $g^{-1}$ including intercepts

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IB Maths AA HL Sl 2 5 Composite and Inverse Functions Questions question 1