###### Answer: A

Wed Aug 15 2001 14:30:00 GMT-0400 (Eastern Daylight Time) · In mathematics an inverse function (or anti- function ) is a function that “reverses” another function : if the function f applied to an input x gives a result of y then applying its inverse function g to y gives the result x i.e. g(y) = x if and only if f(x) = y. The inverse function of f is also denoted as −.. As an example consider the real-valued function …

Wed Sep 18 2002 14:30:00 GMT-0400 (Eastern Daylight Time) · In mathematics the graph of a function f is the set of ordered pairs (x y) where f(x) = y.In the common case where x and f(x) are real numbers these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.. In the case of functions of two variables that is functions whose domain consists of pairs (x y) the graph …

Definitions Graphs and closed graphs . The graph of a function f : X → Y is the set . Gr f ≝ { (x f(x)) : x ∈ X } = { (x y) ∈ X × Y : y = f(x) }. Assumption: If X and Y are topological spaces then X × Y will always be endowed with the product topology.. If X and Y are topological spaces D ⊆ X and f : D → Y is a function then f has a closed graph (resp. sequentially closed …

Inverse function theorem – Wikipedia

Graph of a function – Wikipedia

Graph of a function – Wikipedia

Lipschitz continuity – Wikipedia

In mathematics specifically differential calculus the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely that its derivative is continuous and non-zero at the point.The theorem also gives a formula for the derivative of the inverse function .In multivariable calculus this theorem can be generalized to any …

Functions whose domain are the nonnegative integers known as sequences are often defined by recurrence relations.. The factorial function on the nonnegative integers (↦!) is a basic example as it can be defined by the recur…