Inverse Relation of A Function
A function is invertible if and only if its inverse relation is a function, in which case the inverse relation is the inverse function.
The inverse relation of a function is the relation defined by .
This is not necessarily a function: One necessary condition is that f be injective, since else is multi-valued. This condition is sufficient for being a partial function, and it is clear that then is a (total) function if and only if f is surjective. In that case, i.e. if f is bijective, may be called the inverse function of f.
Read more about this topic: Inverse Relation
Famous quotes containing the words inverse, relation and/or function:
“The quality of moral behaviour varies in inverse ratio to the number of human beings involved.”
—Aldous Huxley (1894–1963)
“The whole point of Camp is to dethrone the serious. Camp is playful, anti-serious. More precisely, Camp involves a new, more complex relation to “the serious.” One can be serious about the frivolous, frivolous about the serious.”
—Susan Sontag (b. 1933)
“If the children and youth of a nation are afforded opportunity to develop their capacities to the fullest, if they are given the knowledge to understand the world and the wisdom to change it, then the prospects for the future are bright. In contrast, a society which neglects its children, however well it may function in other respects, risks eventual disorganization and demise.”
—Urie Bronfenbrenner (b. 1917)