Edexcel IGCSE Math B 4.E composite functions

Practise composite-function questions by substituting one function into another, simplifying the rule and solving equations such as hh(x)=x.

Exam points

Evaluate composite values such as hf(2) by applying the inner function first.
Simplify composite rules such as gh(x) into the requested algebraic form.
Solve equations involving repeated functions, showing clear algebraic working.

[Maximum number: 2]

Figure 3

Information about the function f is shown in Figure 3.
Given that f is the mapping $\mathrm{f}: x \mapsto a x^{3}+b$ where a and b are constants,

Show algebraically that $\operatorname{gg}(x)=x$

Show clear algebraic working.

$g(g(x))=\frac{p\left(\frac{px}{x-p}\right)}{\frac{px}{x-p}-p}$ $=\frac{\frac{p^2x}{x-p}}{\frac{px-p(x-p)}{x-p}} =\frac{p^2x}{x-p}\times\frac{x-p}{p^2}=x$

Marks: M1, A1.

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4.E Composite functions question 1