Final answer:
The statement is False. The limit of a function as x approaches a certain point c can be defined even if the function itself is not defined at x=c. This can occur in cases where the function has an asymptote at x=c.
Step-by-step explanation:
The statement is False. For lim x→c f(x) to be defined, it's not necessary that the function f must be defined at x=c. Limits describe the behavior of a function as it approaches a certain point, not necessarily the value at that point. Consider a function with a hole at a point where x=c; even though the function is not defined at that specific point, the limit as x approaches c may still exist if the function approaches a specific value from both sides.
For example, the function f(x) = 1/x is not defined at x=0, yet as x approaches zero, the limit approaches infinity. Such behavior defines an asymptote, showing that the function need not be defined at the point to have a limit.