Question 34
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
(i) the set $\left\{ \frac{f(x)}{x} \mid x \ne 0 \right\}$ is finite,
(ii) $f(3x - 1 - f(x)) = 3(f(x) - 1 - 3x)$ for all $x \in \mathbb{R}$.
(i) the set $\left\{ \frac{f(x)}{x} \mid x \ne 0 \right\}$ is finite,
(ii) $f(3x - 1 - f(x)) = 3(f(x) - 1 - 3x)$ for all $x \in \mathbb{R}$.