Exam-style question
Try this first
Explain what is meant by the composition of two functions. In your answer, describe the domain and co-domain of g ○ f when f: A → B and g: B → C, and state the order in which the functions are applied.
Model answer
What a good answer should say
- Function composition combines two functions to form a new function.
- For f: A → B and g: B → C, the composition g ○ f has domain A and co-domain C.
- Function f is applied first to an input from A.
- The result is in B and is then used as the input to g, producing a final result in C.
Explanation
Why this works
The intermediate co-domain of f must match the domain of g so that the result returned by f can be used by g. The order is read from right to left: f first, followed by g.
Common mistake
No common mistake is linked to this question yet.