**Composition**

Combining two functions by substituting one function's formula in place of each *x* in the other function's formula. The composition of functions *f* and *g* is written *f*°*g*, and is read aloud "*f* composed with *g*." The formula for *f*°*g* is written (*f*°*g*)(*x*). This is read aloud "*f* composed with *g* of *x*."

Note: Composition is not commutative. That is, (*f*°*g*)(*x*) is usually different from (*g*°*f*)(*x*). The example below illustrates this.

Example:
| ||

^{1}(f°g)(x) | = 3(4x + 1)^{2} + 12(4x + 1) – 1 | |

= 3(16
| ||

^{1}(g°f)(x) | = 4(3x^{2} + 12x – 1) + 1 | |

= 12x^{2} + 48x – 4 + 1= 12 x^{2} + 48x – 3 |

**See also**

Identity of an operation, identity function, inverse, composite

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