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.
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