I understand functions can only be one-to-one or many-to-one ( like f(x) = x^2), is there a reason why we choose to not define functions as one-to-many , for example f(x) = +-sqrt(x). Equations that fail the vertical line test are not functions?
My own thinking on this is that we don't want to get into the habit of saying an input can result in two different outputs, but i don't exactly understand why? Is it some vague idea of being well-defined? lack of ambiguity? Or we can't undo a function that is one-to-many ?
Thoughts would be helpful!
My own thinking on this is that we don't want to get into the habit of saying an input can result in two different outputs, but i don't exactly understand why? Is it some vague idea of being well-defined? lack of ambiguity? Or we can't undo a function that is one-to-many ?
Thoughts would be helpful!