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What is meant by domain of function to be "explicitly defined"?

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In my maths books it's said that: "when the domain of f(x) is not explicitly defined then in this case domain will mean the set of values of x for which f(x) assumes real value"

SO what it meant by domain to be implicitly/explicitly define

And what it the logic behind the above extratc...why we take real values only can't there be any other fields like C ?


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