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In Mathematics , a domain of a ''k''-place Relation ''L'' ⊆ ''X''1 × … × ''X''''k'' is one of the sets ''X''''j'', 1 ≤ ''j'' ≤ ''k''. If ''k'' = 2 and ''L'' ⊆ ''X''1 × ''X''2, then ''L'' is a Function defined as ''L'' : ''X''1 → ''X''2. It is then conventional to call ''X''1 the domain of the function ''L'' and to call ''X''2 the '''codomain''' of ''L''. DOMAIN OF A FUNCTION Given a of ''f''. The . A well defined function must map every element of its domain to an element of its codomain. For example, the function ''f'' defined by : ''f''(''x'') = 1/''x'' has no value for ''f''(0). Thus, the set of Real Number s, , cannot be its domain. In cases like this, the function is either defined on or the "gap is plugged" by explicitly defining ''f''(0). If we extend the definition of ''f'' to : ''f''(''x'') = 1/''x'', for ''x'' ≠ 0 : ''f''(0) = 0, then ''f'' is defined for all real numbers, and its domain is . Any function can be restricted to a Subset of its domain. |
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