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When a function F(x) = x^2 is defined as a mapping from a set N (for example) to N. The set of all natural numbers x can take is domain of the function. So DOMAIN is clearly = N.  
 The set of values of F(x) is the CODOMAIN of F(x).  This is clearly a set of squares of natural numbers and is a SUBSET of N.

Domain is the value of x in a certain function and codomain is a set in which value domain may lie