BdMO National 2013: Secondary 1

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BdMO
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BdMO National 2013: Secondary 1

Unread post by BdMO » 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 $f(2013)$?

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Fatin Farhan
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Re: BdMO National 2013: Secondary 1

Unread post by Fatin Farhan » Sun Jan 12, 2014 5:24 pm

$$f(0)=-f(-1*0)=-f(0)$$.
But this is only possible if $$f(0)=0$$
Now, $$f(0)=f(1)=f(2)=f(3)=.............=f(2013)=0$$
"The box said 'Requires Windows XP or better'. So I installed L$$i$$nux...:p"

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