Question

For what value of the constant c is the function f continuous on (−[infinity],[infinity])?

a) c=0
b) c=1
c) c=−1
d) c=2

Answer 1

The constant c can be any real number for the function to be continuous on the interval (-∞, ∞).

Step-by-step explanation:

To determine the value of the constant c for which the function f is continuous on the interval (-∞, ∞), we need to examine the properties of continuity.

In order for a function to be continuous at a particular point, the limit of the function as x approaches that point from the left must be equal to the limit as x approaches that point from the right, and both limits must be equal to the value of the function at that point.

In this case, the function is given as f(x) = cx, where c is a constant. For the function to be continuous on (-∞, ∞), the limit as x approaches any value must be equal to c times that value. Since both sides approach the same value and the function is linear, the value of c can be any real number. Therefore, the answer is any real number.