Final answer:
The provided statements discuss the concept of testable hypotheses, which relates to scientific validation and not directly to mathematical functions. To be defined at a point, a function must have an output for every input within its domain.
Step-by-step explanation:
The question poses a scenario in which a function being defined or undefined at a certain point is being discussed. However, the fragments provided do not directly pertain to a specific mathematical function or its domain and continuity. Nonetheless, I will focus on the general principles mentioned that may apply to mathematics. For instance, statement (b) "It cannot be proved scientifically because it is not a testable hypothesis" is false in the context that scientific methods rely on the ability to test hypotheses. On the other hand, statement (d), "It cannot be proved scientifically because it is a testable hypothesis", is also false, as the capacity to test a hypothesis is fundamental to scientific validation. When it comes to mathematics and functions in particular, a function being defined at a point generally means that there is a specific output for every input within the function's domain.