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In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

—Wikipedia
Injective∀ a, b ∈ X: f(a) = f(b) ⇒ a = b
Surjective∀ b ∈ Y: ∃ a ∈ X: f(a) = b
Bijective∀ b ∈ Y: ∃ !a ∈ X: f(a) = b

Result

dom(f) =

im(f) =

injective:

surjective:

bijective:

f-1 = {}

dom(f-1) =

im(f-1) =