# 1.16: Composition of Functions

Difficulty Level: At Grade Created by: CK-12
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### Vocabulary Language: English

TermDefinition
composite function A composite function is a function $h(x)$ formed by using the output of one function $g(x)$ as the input of another function $f(x)$. Composite functions are written in the form $h(x)=f(g(x))$ or $h=f \circ g$.
domain The domain of a function is the set of $x$-values for which the function is defined.
Function A function is a relation where there is only one output for every input. In other words, for every value of $x$, there is only one value for $y$.
Function composition Function composition involves 'nested functions' or functions within functions. Function composition is the application of one function to the result of another function.
input The input of a function is the value on which the function is performed (commonly the $x$ value).
Output The output of a function is the result of the operations performed on the independent variable (commonly $x$). The output values are commonly the values of $y$ or $f(x)$.
Range The range of a function is the set of $y$ values for which the function is defined.

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