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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (also known as onto, or a surjection), if for every element y in the codomain Y of f
Injective function
non-surjective function (injection, not a bijection) An injective surjective function (bijection) A non-injective surjective function (surjection, not
Bijection, injection and surjection
the domain. That is, the image and the codomain of the function are equal. A surjective function is a surjection. Notationally: ∀ y ∈ Y , ∃ x ∈ X  such
Bijection
one-to-one function (a.k.a. injective function) (see figures). An injective non-surjective function (injection, not a bijection) An injective surjective function
Twelvefold way
set X is equivalent to counting injective functions N → X when n = x, and also to counting surjective functions N → X when n = x. Counting multisets of
Partial function
A partial function is said to be injective, surjective, or bijective when the function given by the restriction of the partial function to its domain
Inverse function
as: f ( x ) = ( 2 x + 8 ) 3 . {\displaystyle f(x)=(2x+8)^{3}.} A surjective function f from the real numbers to the real numbers possesses an inverse
Identity function
on M is clearly an injective function as well as a surjective function, so it is also bijective. The identity function f on M is often denoted by idM
Function (mathematics)
g(y)=x_{0}} , if y ∉ f ( X ) . {\displaystyle y\not \in f(X).} The function f is surjective (or onto, or is a surjection) if the range equals the codomain
Function composition
In mathematics, function composition is an operation that takes two functions f and g and produces a function h such that h(x) = g(f(x)). In this operation