Let f:R-0 R be a function such that f(x)-6f((1)/(x))=(35)/(3x)-(5)/(2).

Question

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

Accepted Answer

$F(x)-6f(1/x)=\frac{35}{3x}-\frac{5}{2}\,$

$\begin{gathered} =\underset{x	o 0}{lim}(\frac{1}{\alpha x}-2x-\frac{1}{3x}+\frac{1}{2}) \ \alpha =3,\, B=1/2 \ \alpha +2B=3+1=4 \end{gathered}$

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