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Let $f : [0 , \infty) \to \mathbb{R},$ continuous at $ x_0 = 0$ satisfying $$f(3x) - 2x = f(x)$$ Prove that $f(x) = x$.

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    Please show us what you've tried. – 2017-02-02
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    Okay, the question doesn't show effort, but that's too much downvoting. – 2017-02-02
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    All such functions are $f(x)=x+c$. – 2017-02-02
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    Yes,i managed to show that function we searched for had a linear form. – 2017-02-02
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    Well, if you could prove it had a linear form you'd be done. As a hint to get started: suppose you had two such functions, $f(x)$ and $g(x)$. What can you say about $h(x)=f(x)-g(x)$? – 2017-02-02
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    I can scroll down the most recent list and find questions that display no effort, but are upvoted. What influences people's decisions around here? – 2017-02-02
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    @Kaynex There are many accepts, downvotes, upvotes , closevotes, whatsoever on this site, I will never understand. – 2017-02-02
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    Beats me.. If i had a good idea on how the problem was solved i would've written it :/ – 2017-02-02
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    Personally I think this is a good question. You have my upvote. – 2017-02-02

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$f(3x)=2x+f(x) =2x+2x/3+f(x/3) =2x+2x/3+2x/9+f(x/9)$ $2+2/3+2/9+...=2*1/(1-1/3)=3$. By continued on 0 $f(3x)=3x$

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    while editing, please translate into English – 2017-02-02