1thanx risabh for the proof...
\hspace{-16}$Let $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ be a Continuous function and $\mathbf{f(x)=f(2x)\forall x\in \mathbb{R}}.$\\\\ If $\mathbf{f(1)=3}$.Then the value of $\mathbf{\int_{-1}^{1}f(f(x))dx=}$
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4 Answers
1f(x) = 3 satisfies everything so answer has to be 6 :P
but we have to prove that that is the only function
for that see this http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=455520