# question about continuous function.

• Jun 23rd 2011, 01:14 PM
taypen
question about continuous function.
hello,

i got continuous function on $[0,1]$ such that $f(0) = f(1)$ i need to prove that exist "a" such that $f(a) = f(a+0.5)$
$a\in \left[0,\frac{1}{2}\right]$

your help would be much appreciated!
• Jun 23rd 2011, 03:20 PM
emakarov
Re: question about continuous function.
The idea is described in the Wikipedia article about the intermediate value theorem.
• Jun 24th 2011, 12:00 AM
ojones
Re: question about continuous function.
Emakarov is correct. Look at the example at the bottom of the article concerning real world applications. Your problem is just a slight variation: consider the function $g(t)=f(t)-f(t+0.5)$.
• Jun 24th 2011, 06:24 AM
taypen
Thanks
I knew it was something around the intermediate value theory
After reading all the article i found simmilar problem and it's solution.
So thanks for your help.