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:
“Yet time and space are but inverse measures of the force of the soul. The spirit sports with time.”
—Ralph Waldo Emerson (1803–1882)
“To criticize is to appreciate, to appropriate, to take intellectual possession, to establish in fine a relation with the criticized thing and to make it one’s own.”
—Henry James (1843–1916)
“The uses of travel are occasional, and short; but the best fruit it finds, when it finds it, is conversation; and this is a main function of life.”
—Ralph Waldo Emerson (1803–1882)