The controls {f-1(y): y ∊ Y} of a function f: X → Y partition the domain X.
For any particular y ∊ Y, its pre image f -1(y) may be
• Empty
• Consist of a single element
• Consist of many elements
Where f -1(y) consists of one and only one element for every y ∊ Y, the pre image defines a function from Y → X whish is called the inverse function. It is denoted f -l.