Let \(\mathrm{f}: \mathbb{R}-\{0\} \rightarrow \mathbb{R}\) be a function such that \(\mathrm{f}(\mathrm{x})-6 \mathrm{f…

Let \(\mathrm{f}: \mathbb{R}-\{0\} \rightarrow \mathbb{R}\) be a function such that \(\mathrm{f}(\mathrm{x})-6 \mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\frac{35}{3 \mathrm{x}}-\frac{5}{2}\). If the \(\lim _{x \rightarrow 0}\left(\frac{1}{\alpha x}+f(x)\right)=\beta ; \alpha, \beta \in \mathbb{R}\) then \(\alpha+2 \beta\) is equal to

[JEE Main 2025, 24 Jan (Shift 1)]