Question

for what value of the constant c is the function f continuous on (–[infinity], [infinity])? write and use all the parts of the definition of continuity. explain all the steps in your answer

Answer 1

To determine the value of the constant c for which the function f is continuous on (-∞, ∞), we need to consider the definition of continuity. In the case of a continuous probability function, we don't have a specific function provided, so it is not possible to determine a value for the constant c.

Step-by-step explanation:

To determine the value of the constant c for which the function f is continuous on (-∞, ∞), we need to consider the definition of continuity. A function f is continuous at a point c if three conditions are met:

1. lim (x→c) f(x) exists
2. lim (x→c) f(x) = f(c)
3. f is defined at c

Since we are considering the entire interval (-∞, ∞), we need to make sure that the function meets these conditions for every point in that interval. This means that the limit as x approaches c from the left and the limit as x approaches c from the right must exist and be equal, and the value of f(c) must also exist.

In the case of a continuous probability function, we don't have a specific function provided, so it is not possible to determine a value for the constant c. We would need more information about the function to determine its continuity.