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7.11: Inverse Functions

Difficulty Level: At Grade Created by: CK-12
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Vocabulary

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.

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Difficulty Level:

At Grade

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Date Created:

Mar 12, 2013

Last Modified:

Jun 04, 2015
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