If f(x) = begin{cases} x, & 0

Question

(D) To check the continuity at $x = 1/2$,we evaluate the left-hand limit,right-hand limit,and the function value.$1$. Left-hand limit: $\lim_{x 	o 1/

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$f(x)$ is discontinuous at $x = 1/2$

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(D) To check the continuity at $x = 1/2$,we evaluate the left-hand limit,right-hand limit,and the function value.$1$. Left-hand limit: $\lim_{x 	o 1/2^-} f(x) = \lim_{x 	o 1/2^-} x = 1/2$.$2$. Right-hand limit: $\lim_{x 	o 1/2^+} f(x) = \lim_{x 	o 1/2^+} (1 - x) = 1 - 1/2 = 1/2$.$3$. Function value: $f(1/2) = 1$.Since $\lim_{x 	o 1/2^-} f(x) = \lim_{x 	o 1/2^+} f(x) = 1/2$,the limit $\lim_{x 	o 1/2} f(x)$ exists and is equal to $1/2$.However,$\lim_{x 	o 1/2} f(x) = 1/2 
eq f(1/2) = 1$.Therefore,$f(x)$ is discontinuous at $x = 1/2$.

If $f(x) = \begin{cases} x, & 0 < x < 1/2 \\ 1, & x = 1/2 \\ 1 - x, & 1/2 < x < 1 \end{cases}$,then which of the following is true?

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