What conditions of a function [color=#0000ff]y=f(x)[/color] would yield an inverse [color=#ff0000]x=f(y)[/color] relation that also satisfies the definition of "function"?
If function [color=#0000ff]y=f(x)[/color] either never decreases or never increases (including across discontinuities), then no two points on it's graph will have the same y value. Such a function may be referred to as "monotonic."[br]Under such conditions, no two points on the graph of inverse [color=#ff0000]x=f(y)[/color] will have the same x value, and the relation [color=#ff0000]x=f(y)[/color] may therefore also be deemed a function.[br]Vocabulary note: All functions are relations, but not all relations are functions.