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# 7.11: Inverse Functions

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

1-1 function

1-1 function

A function is 1-1 if its inverse is also a function.
composite function

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 $h=f \circ g$.
Function

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 $y$.
Horizontal Line Test

Horizontal Line Test

The horizontal line test says that if a horizontal line drawn anywhere through the graph of a function intersects the function in more than one location, then the function is not one-to-one and not invertible.
inverse

inverse

Inverse functions are functions that 'undo' each other. Formally: $f(x)$ and $g(x)$ are inverse functions if $f(g(x)) = g(f(x)) = x$.
inverse function

inverse function

Inverse functions are functions that 'undo' each other. Formally $f(x)$ and $g(x)$ are inverse functions if $f(g(x)) = g(f(x)) = x$.
Inverse Relation

Inverse Relation

An inverse relation is a relation with output values that are mapped to create input values for a new relation. The input values of the original relation would become the output values for the new relation.
One-to-one

One-to-one

A function is one-to-one if its inverse is also a function.
Relation

Relation

A relation is any set of ordered pairs $(x, y)$. A relation can have more than one output for a given input.
Vertical Line Test

Vertical Line Test

The vertical line test says that if a vertical line drawn anywhere through the graph of a relation intersects the relation in more than one location, then the relation is not a function.

Mar 12, 2013

Jun 04, 2015