` f(x){{:(x^(3) - 3"," if x le 2 ),(x^(2) + 1"," if x gt 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 three 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 LHL, RHL, and \( f(2) \) are all equal.

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