Natural domain

Summary

• Given: a real-valued function of a real variable, \(f: A→B\) where \(A⊆R\) , \( B⊆R\)
• The assignment rule is defined by a formula such as \(f(x)=x^2\)
• The natural domain for the assignment rule is the subset of \(R\) for which the formula is valid.
• For example, the natural domain for the rule defined by \(f(x)=\sqrt{x}\) is \([0,∞)\) while it is all of \(R\) if \(f(x)=x^2\)
• If the domain is not specified , it is given by the natural domain.
• If the codomain is not specified, it is common to either let the codomain be equal to all of \(R\) or as the range of the function.