[algebra.functionComposition.title]
[algebra.functionComposition.description]
Examples: f(x)=x^2, g(x)=x+1
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
Theory & Formula
Function Composition
Function composition combines two functions where the output of one becomes the input of another.
Notation
\((f \circ g)(x) = f(g(x))\)
Read as 'f composed with g of x' or 'f of g of x'
Properties
Not Commutative:
\(f \circ g \neq g \circ f\) (in general)
Associative:
\((f \circ g) \circ h = f \circ (g \circ h)\)
Identity Function:
\(f \circ I = I \circ f = f\) where \(I(x) = x\)
Example
Let f(x) = x² and g(x) = x + 1:
\(f(x) = x^2, \quad g(x) = x + 1\)\((f \circ g)(x) = f(g(x)) = f(x+1) = (x+1)^2 = x^2 + 2x + 1\)\((g \circ f)(x) = g(f(x)) = g(x^2) = x^2 + 1\)
Notice that f∘g ≠ g∘f