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who can explain easily domain, codomain, and range?

MIT 18.03SC Differential Equations
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Suppose we have a function f(x) = y = \[\frac{ x }{ x-3 }\] . Domain of the function will be all possible values of the independant variable 'x' such that the function has a defined value. Here it would be all real numbers except 3. Codomain is all the possible values of 'y' as defined by the question. It is given in the beginning in the form of R -> R (real numbers) Range is a subset of codomain containing only those values of 'y' which satisfy the given function. Here the codomain and range are same but had the function been \[x^{2}\] then the codomain may be real numbers but range would only be positive real numbers. Domain would be all real numbers.
domain is set of permissible input values

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