Question

blah this is making no sense, please help me:

If you switch the domain and range of any function, will the resulting relation always be a function? Explain your answer with examples.

Answer 1

No, it won't be. A function is determined by two collections A and B and an assignment of a unique element of B to each element of A. If you let the function be f(x) = x², and let the domain be -1 to +1, then the range will be 0 to +1. But if you swap the domain and the range over, you'll have each element of the new domain being mapped onto two elements of the new range - so it's no longer a mapping to a unique element.