`f(x)=2x+3` if `x<= 2` and `f(x)=2x-3` if `x > 2` check continuity of f(x) at x =2.

Explanation

To check the continuity of the function \( f(x) \) at \( x = 2 \), we need to verify the following conditions:

1. The function \( f(2) \) is defined.
2. The left-hand limit (LHL) as \( x \) approaches 2 exists.
3. The right-hand limit (RHL) as \( x \) approaches 2 exists.
4. The left-hand limit and right-hand limit are equal, and both are equal to \( f(2) \).

### Step 1: Find \( f(2) \)
...