15.2. THEOREM. Let a be a point in the domain D of the function f. The following statements are equivalent: (a) f is continuous at a. (b) If e is any positive real number, there exists a positive number 8(e) such that if x € D and x – al < ô(e), then |f(x) - f(a)| < e. (c) If (xn) is any sequence of elements of D which converges to a, then the sequence (f(xn)) converges to f (a).

Let f and g be functions. (a) The function (f+g)(x) is defined for all values of x that are in the domains of both _______ and_______. (b) The function (fg)(x) is defined for ail values of x that are in the domains of both ________ and_________ . (c) The function (f/g)(x) is defined for all values of x that are in the domains of both ________and________, and g(x) is not equal to ________.