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)

thami says:

October 6, 2015 at 12:49 pm

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- TrueBeautyOfMath says:
  
  October 7, 2015 at 4:03 pm
  
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