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Math Help - Function

  1. #1
    Junior Member
    Joined
    Aug 2009
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    Function

    Hi everybody,

    I must show that there is a function f continious in  [0,2\pi[, inconstant and

    different from the function x{\longrightarrow} x such as:

     (\forall (x;y)\in [0;2\pi[^2)\  cos(x-y) \le cos(f(x)-f(y))

    I don't know anything to do, can you help me please?

    And thank you anyway.
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  2. #2
    ynj
    ynj is offline
    Senior Member
    Joined
    Jul 2009
    Posts
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    Quote Originally Posted by lehder View Post
    Hi everybody,

    I must show that there is a function f continious in  [0,2\pi[, inconstant and

    different from the function x{\longrightarrow} x such as:

     (\forall (x;y)\in [0;2\pi[^2)\ cos(x-y) \le cos(f(x)-f(y))

    I don't know anything to do, can you help me please?

    And thank you anyway.
    An tricky answer:f(x)=x-1
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