I can assert that a mapping is continuous. I can then use the assertion to determine the characteristics of a formulation of that mapping.
>> >> (d) Does lim (x->3) f(x) exist? >> >> answer: Yes, the limit is 6. >> >> (d) Does there exist a function g continuous on the set of >> real numbers such that g(x) = f(x) for all x != 3? >> >> answer: Yes, the function g(x) = x + 3 has that property, >> and in fact, it's the only such function. >> [...] >