Let $f : \mathbb{R} - \{0, 1\} \to \mathbb{R}$ satisfy $f(x) + f\left(\frac{1}{1-x}\right) = 1 + x$. Then $f(2)$ equals:
Step-by-Step Solution
Key Concept: Write the equation at $x = 2$, at $x = -1$ (i.e. $1/(1 - 2)$), and at $x = 1/2$. This gives three equations in $f(2), f(-1), f(1/2)$ — solve the linear system.
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Correct Answer: (3)