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If $f(x)=\left\{\begin{array}{l}x, \text { when } 0 \lt x \lt 1 / 2 \\ 1, \text { when } x=1 / 2 \\ 1-x, \text { when } 1 / 2 \lt x \lt 1\end{array}\right.$ then

MathematicsContinuity and DifferentiabilityJEE Main

Options:

A $\lim _{x \rightarrow 1 / 2}^{+} f(x)=2$
B $\lim _{x \rightarrow 1 / 2}^{-} f(x)=2$
C $f(x)$ is continuous at $x=\frac{1}{2}$
D $f(x)$ is discontinuous at $x=\frac{1}{2}$

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