Year 11 - Maths
Solving equations involving 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 solve equations involving composite functions.
Key Notes
- A composite function may have a given output.
- It is possible to solve to find the input.
- This can be extended to two composite functions that have a common output.
Vocabulary To Learn
- Function: A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
- Equation: An equation is used to show two expressions that are equal to each other.
Common Mistakes To Avoid
- Confusing the order in which functions are evaluated.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A composite function may have a given output. It is possible to solve to find the input.
2. Use this key word in a maths sentence and explain it clearly. 'Function'
A function is a mathematical relationship that uniquely maps values of one set to the values of another set. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Confusing the order in which functions are evaluated. Correction: Pupils can substitute their answer into the composite function to check their answer. Putting brackets around the functions can help with confirming the order.
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 functions Study Guide
- Writing a generalised statement about specific number properties Study Guide
- Writing a proof Study Guide
- Writing composite functions Study Guide
Browse all guides in the Year 11 Maths guide library.