Final answer:
Continuity of a function at one point does not ensure continuity at another unless the function is continuous over the entire interval. In continuous probability density functions, the probability is the area under the curve for a given range.
Step-by-step explanation:
If a function f is continuous at x = 0 and x = 2, it does not necessarily mean that f is continuous at x = 1. Continuity at one point does not automatically imply continuity at another, unless the function is known to be continuous on the entire interval that includes both points. In probability theory, for a continuous probability density function, the probability is equivalent to the area under the curve of f(x) within a specified range. Therefore, to determine P(0 < x < 12) for f(x), we look at the area under f(x) from 0 to 12. If f(x) is a horizontal line at f(x)=12, then P(0 < x < 12) would be the area under this line, over the interval from 0 to 12.