At x =1, the function given by `f(x) = {(x,x lt 1),(2x-1,x ge1):}` is
(a) Continuous
(b) Not continuous
( c) Not defined

Explanation

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

1. The value of the function at \( x = 1 \), denoted as \( f(1) \).
2. The limit of the function as \( x \) approaches 1 from the left, denoted as \( \lim_{x \to 1^-} f(x) \).
3. The limit of the function as \( x \) approaches 1 from the right, denoted as \( \lim_{x \to 1^+} f(x) \).

### Step-by-Step Solution:

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