I am reading about when to function are equal or identical. As per the source through which i am studying two function f and g are equal and identical if they satisfy following conditions.
1) Domain of f should be equal to Domain of g.
2) Range of f should be equal to Range of g.
3) f(x)=g(x), for every x belonging to their common domain.
I am little confused with third condition, let D denote the Domain of function f , as per the condition 1 if g is equal to f then the domain of g is D itself.
So common domain will be D. So instead of writing Domain of f or Domain g why they have used the word common domain or I am missing some crucial point?
My another question is, are these three condition are necessary but not sufficient for stating to function are equal?