Art of Problem Solving
Chapter 2: 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.
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.