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Derivative of Some Standard Functions

If f x = left...

Question

If $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x, & w h e n 0 < 1 / 2 1, & w h e n x = 1 / 2 1 - x & w h e n 1 / 2 < x < 1 \end{matrix}$ , then

A

l i m_{x \to 1 / 2 +} f (x) = 2

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B

l i m_{x \to 1 / 2 -} f (x) = 2

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C

f (x) i s c o n t i n u o u s a t x = \frac{1}{2}

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D

f (x) i s d i s c o n t i n u o u s a t x = \frac{1}{2}

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Solution

The correct option is D $f (x) i s d i s c o n t i n u o u s a t x = \frac{1}{2}$
Since, $l i m_{x \to 1 / 2} f (x) \neq f (\frac{1}{2})$

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