Question

consider the following. f(x) = 9x − cos x find the x-value at which f is not continuous. is the discontinuity removable? (enter none in any unused answer blanks.)

Answer 1

A function is not continuous at a specific x-value if one of three conditions is met: removable discontinuity, jump discontinuity, or essential discontinuity. In the given function f(x) = 9x − cos x, there are no obvious x-values at which the function is not continuous. Therefore, the function is continuous for all values of x.

Step-by-step explanation:

A function is not continuous at a specific x-value if one of three conditions is met:

1. The function has a removable discontinuity, which means that the function can be made continuous by redefining the function at that particular x-value.
2. The function has a jump discontinuity, which means that the left-hand and right-hand limits of the function at that x-value exist, but they are not equal.
3. The function has an essential discontinuity, which means that either the left-hand or right-hand limit does not exist or is infinite.

In the given function f(x) = 9x − cos x, there are no obvious x-values at which the function is not continuous. Therefore, the function is continuous for all values of x.