Function composition

High school (ages 12+)
Mathematics & Numbers

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/function-composition

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the generalization?Function composition is a special case of the composition of relations
2. How do you write a composed function?We use the symbol ∘. If f goes from A to B and g goes from B to C, then g ∘ f means first use f, then g. The result is a function from A to C.
3. Why is the order important in function composition?Because g ∘ f usually gives a different answer than f ∘ g. The first machine's output becomes the second machine's input, so swapping them changes the result.

Function: A mapping from a set of inputs (domain) to a set of outputs (codomain) where each input corresponds to exactly one output.
Composition Operator (∘): A binary operator that combines two functions, applying one after the other to produce a new function.
Associativity: A property where the grouping of operations does not affect the final result, as in (a b) c = a (b c).