<s>[INST] Interesting functional equations problem? $f(x) + 3 f\left( \frac {x-1}{x} \right) = 7x$ 
Find all functions $f:\mathbb R \to \mathbb R$ that satisfy $f(x)  + 3 f\left( \frac {x-1}{x} \right) = 7x$.

How would we solve this? I noticed that if you plug in $\frac{x-1}{x}$ in for $x$, and then again, we can solve $f(x)$ after bashing it out with systems of equations. However, the resulting function has a few values for which it is undefined. I tried finding those values by going back to the original equation, but it doesn't seem like a "good" answer. Since I then wanted to verify that I had the correct function first, I plugged the actual function back into the original equation. However, the LHS and RHS didn't match up. Is there a better way to solve this other than just bashing?
Thanks in advance!
 [/INST] Sorry, this wouldn't fit into a comment, so I had to post this in as an answer, but when I plugged $f$ back into the original equation, I got:
\begin{align*}
f(x) + 3 f\left(\frac{x-1}{x}\right) &= \frac{1}{28}\left(x - 3 - \frac{3}{x} - \frac{9}{x-1}\right) + 3\left(\frac{1}{28}\right)\left(\frac{x-1}{x} - 3 - \frac{3}{\frac{x-1}{x}} - \frac{9}{\frac{x-1}{x}-1}\right)\\
&= \left(\frac{1}{28}\right)\left(x - 3 - \frac{3}{x}-\frac{9}{x-1}+3\left(\frac{x-1}{x}-3-\frac{3x}{x-1}+9x\right)\right)\\
&= \left(\frac{1}{28}\right)\left(x - 3 - \frac{3}{x}-\frac{9}{x-1}+\frac{3x-3}{x} - 3 - \frac{9x}{x-1} + 27x\right)\\
&= \left(\frac{1}{28}\right)\left(28x - 6 + \frac{3x-6}{x}-\frac{9+9x}{x-1}\right)\\
&= \left(\frac{1}{28}\right)\left(28x^3-28x^2-6x^2+6x-3x^2+6x+3x+6-9x+9x^2\right)\\
&= \left(\frac{1}{28}\right)\left(28x^3-28x^2+6x+6\right)\\
&= x^3-x^2+\frac{3x}{14} + \frac{3}{14},
\end{align*}
which doesn't match the given $7x$. If you could tell me where I made my mistake, it would be greatly appreciated. Thanks in advance!
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