A function \(f(x)\) is continuous in the interval [0,2]. It is known that…

GATE · 2014 · CS · Set 1 · Computer Science & IT

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

  1. A.

    There exists a yyin the interval (0,1) such that f(y)=f(y+1)f(y) = f(y+1)

  2. B.

    For every yyin the interval (0,1), f(y)=f(2−y)f(y) = f(2-y)

  3. C.

    The maximum value of the function in the interval (0,2) is 1

  4. D.

    There exists a yyin the interval (0,1) such that f(y)=−f(2−y)f(y) = -f(2-y)

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