الدالة التباينية هي الدالة التي تبقى بها العناصر متباينة (متفاوتة): فبها لا تقترن العناصر المتباينية من مجالها بنفس العنصر من مجالها المقابل. بمعنى أن كل عنصر من مجالها المقابل مقترن بعنصر من مجالها واحد على الأقل.
Injective functions. Diagramatic interpretation in the Cartesian plane, defined by the mappingf : X → Y, where y = f(x), X = domain of function, Y = range of function, and im(f) denotes image of f. Every one x in X maps to exactly one unique y in Y. The circled parts of the axes represent domain and range sets – in accordance with the standard diagrams above.
Not an injective function. Here X1 and X2 are subsets of X, Y1 and Y2 are subsets of Y: for two regions where the function is not injective because more than one domain element can map to a single range element. That is, it is possible for more than onex in X to map to the samey in Y.
Making functions injective. The previous function f : X → Y can be reduced to one or more injective functions (say) f : X1 → Y1 and f : X2 → Y2, shown by solid curves (long-dash parts of initial curve are not mapped to anymore). Notice how the rule f has not changed – only the domain and range. X1 and X2 are subsets of X, Y1 and Y2 are subsets of R: for two regions where the initial function can be made injective so that one domain element can map to a single range element. That is, only one x in X maps to one y in Y.