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Let $f:[-1,\sqrt{7}]\rightarrow \mathbb{R}$ be an integrable function with $f(2x)+f(3x)-5f(x)=5[x]-[2x]-[3x], \forall x\in [-1,\sqrt{7}].$
Calculate $\int_{-1}^{\sqrt{7}}f(x)dx $.

My attempt:
Let $g(x)=f(x)+[x]$. Then $g(2x)+g(3x)=5g(x)$.
Let $h(n)=g(nx)-ng(x)$. Then $h(2)+h(3)=0.$

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    If you say that the domain of $f$ is $[-1,\sqrt 7]$, how can you talk about $f(3x)$ for $x=\sqrt 7$ for example? – 2017-02-06
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    I noticed that issue, too...however,ignoring that, what should I do next? – 2017-02-06

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