The mapping of 'f' is said to be onto if every element of Y is the f-image of at least one element of X. => f Y that is range is not a proper subset of co-domain. Mapping (when a function is represented using Venn-diagrams then it is called mapping), defined between sets X and Y such that Y has at least one element 'y' which is not the f-image of X are called into mappings. One-to-one mapping is called injection (or injective). Graphically, if a line parallel to x axis cuts the graph of f(x) at more than one point then f(x) is many-to-one function and if a line parallel to y-axis cuts the graph at more than one place, then it is not a function. While x → x 2, x ε R is many-to-one function. no two elements of A have the same image in B), then f is said to be one-one function. Relation vs Function From high school mathematics onwards, function becomes a common term. If for each x ε A there exist only one image y ε B and each y ε B has a unique pre-image x ε A (i.e. Consider the function x → f(x) = y with the domain A and co-domain B. IIT JEE Coaching For Foundation Classesįunctions can be classified according to their images and pre-images relationships.Structural Organisation in Plants and Animals.
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