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A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true?

  1. There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ 
  2. For every $y$ in the interval $(0,1)$,$f(y)$ = $f(2-y)$
  3. The maximum value of the function in the interval $(0,2)$ is $1$
  4. There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$

11 Answers

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Option A is Correct but D is Wrong ,

Reason

The difference between y and 2-y should be less than the length of the interval given .
Difference between y and 2-y is 2 and length of interval is (0,1)
Therefore D is Wrong
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This Answer contains the all concept in which students having doubt and the usefull comments are also included

so that the correct answer is option A and D.

Answer:

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