## Art of Problem Solving

## Chapter 2: Functions

## Invertible Functions:

Determining if a function is invertible:

*A function is invertible only when there is one input for an output.

*Each of the members of the domain correspond to a unique member of the range.

*We say a function is invertible if it has an inverse.

## Inverse Functions:

What is the Domain of a Function

*Domain is the set of things you can put into a function.

*Range is the set of all possible values of a function.

*If a function has the same output for two different inputs, then the function has no inverse.

*If a function has one output for every input the function has an inverse.

*A function has an inverse if and only if a horizontal line doesn’t exist that passes through more than one point on the graph of the function.

*If the function f has an inverse it is the reflection of the graph over the line x=y.

You must log in to post a comment.