At x =1, the function given by `f(x) = {(sinx,x lt 0),(2x,x ge 0):}` 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 three conditions:

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

The function is defined as:
\[
...