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Function can be easily defined with the help of the concept of mapping. Let X and Y be any two non-empty sets. “A function from X to Y is a rule or correspondence that assigns to each element of set X, one and only one element of set Y”. Let the correspondence be ‘f’ then mathematically we write f: X→Y where y = f(x), x ∈ X and y ∈ Y. We say that ‘y’ is the image of ‘x’ under ‘f ‘ (or x is the pre image of y).
A mapping f: X→Y is said to be a function if each element in the set X has it’s image in set Y. It is possible that a few elements in the set Y are present which are not the images of any element in set X.
Every element in set X should have one and only one image. That means it is impossible to have more than one image for a specific element in set X. Functions can’t be multi-valued (A mapping that is multi-valued is called a relation from X to Y)
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