BdMO National 2013: Secondary 1
Posted: Fri Jan 10, 2014 1:33 am
If $f: \mathbb R \mapsto \mathbb R$ is a function such that $f(x)=-f(-x)=f(x+1)$ for all real $x$, then what is the value of $f(2013)$?
$$f(0)=-f(-1*0)=-f(0)$$.
But this is only possible if $$f(0)=0$$
Now, $$f(0)=f(1)=f(2)=f(3)=.............=f(2013)=0$$
But this is only possible if $$f(0)=0$$
Now, $$f(0)=f(1)=f(2)=f(3)=.............=f(2013)=0$$