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# 3.2: One-to-One Functions and Their Inverses

Difficulty Level: At Grade Created by: CK-12
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Practice One-to-One Functions and Their Inverses

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### Vocabulary Language: English

1-1 function

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

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

invertible

A function is invertible if it has an inverse.

One-to-one

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

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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