show that the function f(x)= 3x^2+2x-1 is continous for x=2

To show that the function f(x) = 3x^2 + 2x - 1 is continuous at x = 2, we need to verify the following three conditions of continuity:

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

Let's go through these steps:

1. The function f(x) = 3x^2 + 2x - 1 is a polynomial function, which is defined for all real numbers, so it is defined at x = 2.

2. To find the limit of f(x) as x approaches 2, we simply substitute 2 into the function:

   lim (x->2) f(x) = 3(2)^2 + 2*2 - 1 = 12 + 4 - 1 = 15

3. Now, we calculate f(2):

   f(2) = 3(2)^2 + 2*2 - 1 = 12 + 4 - 1 = 15

Since the limit of f(x) as x approaches 2 is equal to f(2), we can conclude that the function f(x) = 3x^2 + 2x - 1 is continuous at x = 2.