Is f (x) = 0 the only function that is both odd and even? Except for other function forms with different domain!

Is f (x) = 0 the only function that is both odd and even? Except for other function forms with different domain!

F (x) = f (- x); - f (x) = f (- x); the sum of the two formulas is: F (- x) = 0 = f (x), so it must be f (x) = 0; it should be noted that the domain of definition is symmetric, not necessarily the entire real number field. However, the functions of different domains, although the expression is the same, can not be said to be the same function, so it is odd