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Understanding Functions: Definition, Domain, and Range in Mathematics

A function f from a set X to a set Y represents a relation where every element in the domain (Dom(f) = X) is associated with exactly one element in the range (Rng(f) = Y). For instance, if we have pairs (x, y) and (x, y) where f is applied, then y remains constant for the same x. In this example, the domain Dom(f) is the set {a, b, c, d} and the range Rng(f) consists of the values {1, 3, 5}. The function maps values such that f(a) = 3, f(b) = 3, f(c) = 5, and f(d) = 1.

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Understanding Functions: Definition, Domain, and Range in Mathematics

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    1. Functions A function f from X to Y (in symbols f : X ? Y) is a relation from X to Y such that Dom(f) = X and if two pairs (x,y) and (x,y) ? f, then y = y Example: Dom(f) = X = {a, b, c, d}, Rng(f) = {1, 3, 5} f(a) = f(b) = 3, f(c) = 5, f(d) = 1.

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