Mathematics Question from JEE Main 2025 · 24 January, Shift 1

Let $f : \mathbb{R} - \{0\} \to \mathbb{R}$ be a function such that

$$f(x) - 6f\left(\frac{1}{x}\right) = \frac{35}{3x} - \frac{5}{2}.$$

If $\lim_{x \to 0} \left( \frac{1}{\alpha x} + f(x) \right) = \beta$, then $\alpha, \beta \in \mathbb{R}$, and $\alpha + 2\beta$ is equal to: