Year 11 - Maths
Writing composite functions
Functions and proof
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will further develop their understanding of algebraic notation and graphs by learning about functions, their inverses and composite functions.
Lesson Summary
You will learn to write a composite function both numerically and algebraically.
Key Notes
- 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.
Vocabulary To Learn
- 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 Mistakes To Avoid
- Pupils may try to evaluate composite functions by working from left to right.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Using function notation, you can write a composite function. Function notation can be replaced with the algebraic form.
2. Use this key word in a maths sentence and explain it clearly. '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($$x$$). Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may try to evaluate composite functions by working from left to right. Correction: 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.
More Lessons In This Unit
- Checking and securing understanding of functions Study Guide
- Defining function notation Study Guide
- Finding the inverse of a function Study Guide
- General algebraic forms for specific number properties Study Guide
- Logical arguments Study Guide
- Making conjectures about patterns and relationships Study Guide
- Multiple approaches to logical arguments Study Guide
- Problem solving with functions and proof Study Guide
- Proving or disproving a statement Study Guide
- Solving equations involving composite functions Study Guide
- Solving equations involving functions Study Guide
- Writing a generalised statement about specific number properties Study Guide
- Writing a proof Study Guide
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