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A mathematical function is a rule associating input values to output values. The possible input values to which the function can be applied is an important part of the definition of the function, and the possible output values obtainable from applying the function to valid input values is an important characteristic of the function.
The domain of a function  is the set of all values of the input (independent) variable at which the function is defined.
The range of a function  is the set of all values which can be obtained by applying  to values in its domain.
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