Summary: function is not zero. Viz., if f(x) and g(x) are continuous at x = a, f(x)/g(x) is continuous at x = a, given that g(a) ≠ 0. Proof follows the logic similar to the above cases, based on the limit theorem [§ 2°8(iii)]. (iii) Composite function of two continuous functions is a continuous function; i.e., if f(x) and g(x) are continuous functions at x = a, then f(g(x)) is continuous at x = a. This can be proved by unfolding the definition of continuity as a chain of limits, proving the composite function's continuity. 

Overall, continuity of a function at a point is characterized by the existence of the function value at that point and the convergence of function values as the input approaches the specific point, guaranteeing a seamless transition between values.