- #1

- 3

- 0

I'm usually not convinced when books claim to have found the natural domain of certain functions. For instance, this book I've been reading has defined the natural domain of a function as the largest set of elements whose range is in the real numbers set.

Ever since I've been having trouble accepting that the domain of functions such as f(x) = x² is ℝ.

Should I give [itex]\sqrt{-1}[/itex] as input value, the function would return -1, which is a real number. Therefore, I would be taken into accepting that the domain would be at least ℝ[itex]\cup[/itex]{[itex]\sqrt{-1}[/itex]}, for its range is still ℝ. What should be the bound when looking for a function's domain?

Thanks in advance,

d1ngell