Continuous Function at a Point? Based on Limits

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The Definition of Continuity at a Point is "A function of f is continuous at a point c is f exists at c and (the limit of f(x) as x approaches c from the left) = (the limit of f(x) as x approaches c from the right) = (f(c))"

My problem with this is I don't know enough to know whether they're trying to trick me by omitting the knowledge if the two limits equal f(1) and, because that's omitted, I should answer with "The point at f(c) does not necessarily exist." or what..

Could someone explain this to me? Thanks.