`f(x)= {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):}` Check continuity of f(x) at x = 1.

Explanation

To check the continuity of the function \( f(x) \) at \( x = 1 \), we need to verify the following condition:

\[ \text{For } f(x) \text{ to be continuous at } x = 1, \text{ it must hold that: } \lim_{x \to 1^-} f(x) = \lim_{x \to 1^+} f(x) = f(1) \]

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

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