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AOPS Intermediate Algebra Notes

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.