Writing composite functions
I can write a composite function both numerically and algebraically.
Writing composite functions
I can write a composite function both numerically and algebraically.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Using function notation, you can write a composite function.
- Function notation can be replaced with the algebraic form.
- An input can be substituted in and the numerical output found.
Keywords
Composite function - The composite function gf($$x$$) is the combination of f($$x$$) and g($$x$$). The output from f($$x$$) is the input for g($$x$$).
Common misconception
Pupils may try to evaluate composite functions by working from left to right.
Remind pupils that they cannot do this as each function needs an input and with composite functions the input needs to be evaluated before it can be used.
To help you plan your year 11 maths lesson on: Writing composite functions, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Writing composite functions, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Functions and proof unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
Exit quiz
6 Questions
$${\text{fg}}(8)$$ -
The output of $${\text{g}}(8)$$ being input in to $${\text{f}}(x)$$
$${\text{gf}}(8)$$ -
The output of $${\text{f}}(8)$$ being input in to $${\text{g}}(x)$$
$${\text{hg}}(8)$$ -
The output of $${\text{g}}(8)$$ being input in to $${\text{h}}(x)$$
$${\text{gh}}(8)$$ -
The output of $${\text{h}}(8)$$ being input in to $${\text{g}}(x)$$
$${\text{ff}}(8)$$ -
The output of $${\text{f}}(8)$$ being input in to $${\text{f}}(x)$$