Prove there is no function with the following property:

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I have a function $f:R\rightarrow R$ and I have to prove that there is no $f$ for which $f(f(x))=-2x+1$. First of all I assumed that $f$ is a linear function $f(x)=ax+b$, but I don't think this situation is general enough to prove it's true for any particular cases. I don't know from where I should start. Thank you!