Final answer:
The function F(x)=1/e^x is continuous on the interval (-∞, ∞), meaning it is continuous for all real numbers, as the exponential function e^x is continuous everywhere without any breaks, discontinuities, or undefined points.
Step-by-step explanation:
The function given is F(x)=1/e^x. This function is a mathematical representation of a continuous probability density function in this context. To determine the intervals where F(x) is continuous, we observe that the exponential function e^x is continuous for all real values of x, and so is any constant multiple of it, including when that constant is 1.
Since the exponential function does not have any breaks, discontinuities, or points at which it is undefined, the function F(x) = 1/e^x is continuous for all real numbers. Therefore, F(x) is continuous on the interval (-∞, ∞) or, in other words, for all real numbers. In the context of probability theory, we often restrict the domain to a certain interval for practical reasons, but mathematically, the function is continuous everywhere.