Function:
Function may be simply defined with the help of the theory of mapping. Suppose X and Y be any two non-empty sets. "A function from Y to X is a standard or connection that given to each and every element of set Y, one and single element of set X". Take the connection be 'f' then functionally we may define f: X → Y where y = f(x), x ∈ X and y ∈Y. We can that 'y' is the image of 'x' under 'f ' or x is the pre image of y.
- A mapping f: X → Y is called as function if each and every element in the set X has it's reflection in set Y. It is feasible that a few elements in the set Y are shown which are not the reflections of any elements in set X.
- Each and every element in set X could have one and only one image. That denotes it is not possible to have more than one image for a particular component in set X. Functions may not be multi-valued. A mapping that is multi-valued is known as relation from X to Y
Problem:
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Consider X = {1, -1, 2, 3, -3}, Y = {1, 4, 9, 10,11}. The principle f provided by y = x2 is a function from X to Y. Domain f = X = {1, -1, 2, 3, -3} Range f = {1, 4, 9}
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