hello,

i got continuous function on $\displaystyle [0,1]$ such that $\displaystyle f(0) = f(1)$ i need to prove that exist "a" such that $\displaystyle f(a) = f(a+0.5)$

$\displaystyle a\in \left[0,\frac{1}{2}\right]$

your help would be much appreciated!