Check the continuity of the function f(x) = 3x - 7 at x = 7

To check the continuity of the function f(x) = 3x - 7 at x = 7, we need to verify three conditions:

1. The function f(x) is defined at x = 7.
2. The limit of the function as x approaches 7 exists.
3. The value of the function at x = 7 is equal to the limit of the function as x approaches 7.

Let's check these conditions one by one:

1. The function f(x) = 3x - 7 is defined for all real numbers, including x = 7. So, the first condition is satisfied.

2. The limit of the function as x approaches 7 can be found by substituting x = 7 into the function:

   lim (x->7) [3x - 7] = 3*7 - 7 = 14

   So, the limit exists and is equal to 14. The second condition is satisfied.

3. The value of the function at x = 7 is f(7) = 3*7 - 7 = 14.

   So, the value of the function at x = 7 is equal to the limit of the function as x approaches 7. The third condition is satisfied.

Since all three conditions are satisfied, the function f(x) = 3x - 7 is continuous at x = 7.