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In mathematics . a function is a relation  between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x2, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is –3, then the output is 9, and we may write f(–3) = 9.

The input to a function is often called the argument and the output is often called the value. Inputs and outputs need not be numbers – they can  be elements of any set , for instance geometric figures. For example, a function could associate a triangle with the number 3, a square with the number 4, and so on.

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