Let f: R - \0 → R be a function such that f(x) - 6 f(1/x) = 35/3x - 5/2. If the lim x → 0 (1/(α x) + f(x)) = β; α, β R, then α + 2β is equal to

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q63

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f: \mathbb{R} - \{0\} \rightarrow \mathbb{R}

be a function such that

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