In this mathematics lesson students learn how to find the output of composite functions using the correct notation. As learning progresses they are challenged to generalise outputs in terms of x.

**Differentiated Learning Objectives**

- All students should be able to use a function machine to break down the composite functions in the form gf(x).
- Most students should be able to generate outputs from composite functions and realise that fg(x) does not give the same output as gf(x).
- Some students should be able to use algebra to determine the input of a composite function when given the output.

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