<s>[INST] Functional equation to determine $f(-1)$ 
There's a function $f$ satisfying: 

$$f\left(\frac{1}{1−x}\right)+2\cdot f\left(\frac{x−1}{x}\right)=3x$$

Find the value of $f(−1)$.

I have no idea how to solve this one. If anyone could help me to understand it, I would be grateful.
 [/INST] set $x = -1$ into to the formula of $f$:
$$f\left(\frac{1}{1−x}\right)+2\cdot f\left(\frac{x−1}{x}\right)=3x $$
you'll have for $x = -1$:
$$f\left(\frac{1}{1−(-1)}\right)+2\cdot f\left(\frac{(-1)−1}{(-1)}\right)=-3$$
$$ = f\left(\frac{1}{2}\right)+2\cdot f\left(2\right)=-3$$
Notice that the denominator of is different then $0$
and for $x = \frac{1}{2}$:
$$f\left(2\right)+2\cdot f\left(-1\right)=1.5 $$
 for $x=2$:
$$f(-1)+2\cdot f\left(\frac{1}{2} \right)= 6 $$
Then: 
$f(-1) = 6 - 2f\left(\frac{1}{2} \right) = \frac{-f(2)}{2} + \frac{3}{4}$ ,
 as $ \ -2f\left(\frac{1}{2} \right) = 4f(2) + 6 $ 
Therefore $f(2) = -2.5 \ \Longrightarrow \ f(-1) = \frac{-2.5}{-2} + \frac{3}{4} = 2$ 
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