Function Composition
Apply one function after another.
Key idea
Apply one function after another.
In depth
(f ∘ g)(x) = f(g(x)): apply g first, then feed its output into f. Order matters, because the functions act in sequence.
Worked example
f(x) = 2x, g(x) = x + 3: f(g(x)) = 2(x + 3) = 2x + 6, but g(f(x)) = 2x + 3.
Formula
Real-world uses
- Applying a currency conversion followed by a tax to find the final price
- Chaining steps in code
Common mistake
Assuming f(g(x)) = g(f(x)).
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Function Composition?
Apply one function after another. It is a topic at the advanced level in Algebra.
What is the formula for Function Composition?
The key formula is (f∘g)(x) = f(g(x)).
Where is Function Composition used in real life?
Real-world examples: Applying a currency conversion followed by a tax to find the final price; Chaining steps in code.
What should I learn before Function Composition?
Make sure you are comfortable with Function Transformations, the previous topic in Algebra.
What is a common mistake with Function Composition?
Assuming f(g(x)) = g(f(x)).
How can I practise Function Composition?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Function Composition?
Move on to Inverse Functions next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.