In mathematics, a function is a relationship between a set of inputs and a set of possible outputs, where each input is related to exactly one output. Functions are essential for formulating physical relationships in the sciences and are ubiquitous in mathematics. The modern definition of a function was first given in 1837 by the German mathematician Peter Dirichlet. Functions are denoted by symbols such as f(x), g(x), or P(x), where x is the input. The general representation of a function is y = f(x) . The key components of a function include:
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Domain: The set of inputs for which the function is defined.
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Range: The set of possible outputs that the function can produce.
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Rule: The relationship between the inputs and outputs, which can be represented by a formula, table, or graph.
Functions can be classified into various types, such as polynomial functions, inverse functions, and surjective functions. They are used in various fields, including algebra, geometry, calculus, physics, chemistry, and engineering.
