1. ## 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.

2. Originally Posted by lehder
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.