# Definition: Composition (of functions)

Definition: Let $f:A\rightarrow B$ and $g:B\rightarrow C$ be two functions, with their domains and codomains as written.  The composition of $f$ and $g$, denoted by $g\circ f$, is the function $g\circ f: A\rightarrow C$ that takes $a\in A$ to $g(f(a))\in C$—this last phrase is often denoted by $a\mapsto g(f(a))$.  In other words, $g\circ f(a)=g(f(a))$.

This is an extremely important definition, and for more details check out lesson 31!

### 2 Responses to Definition: Composition (of functions)

1. thami says:

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• My pleasure! I’m glad to hear that you like site 🙂 And if you like the site then I’m sure you’ll also like the book that just got published, see the most recent blog post for a link to it (it’s also on Amazon now too). I hope you continue to enjoy! 🙂 🙂