Let 3f(x) - 2f(1/x) = x, then f'(2) is equal | vedclass

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(B) Given equation is $3f(x) - 2f(1/x) = x$ .....$(i)$Replace $x$ with $1/x$ in equation $(i)$:$3f(1/x) - 2f(x) = 1/x$Rearranging the terms,we get:$-2

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$1/2$

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(B) Given equation is $3f(x) - 2f(1/x) = x$ .....$(i)$Replace $x$ with $1/x$ in equation $(i)$:$3f(1/x) - 2f(x) = 1/x$Rearranging the terms,we get:$-2f(x) + 3f(1/x) = 1/x$ .....$(ii)$To eliminate $f(1/x)$,multiply equation $(i)$ by $3$ and equation $(ii)$ by $2$,then add them:$9f(x) - 6f(1/x) = 3x$$-4f(x) + 6f(1/x) = 2/x$Adding these two equations:$5f(x) = 3x + \frac{2}{x}$$f(x) = \frac{3x}{5} + \frac{2}{5x}$Now,differentiate $f(x)$ with respect to $x$:$f'(x) = \frac{3}{5} - \frac{2}{5x^2}$Substitute $x = 2$ to find $f'(2)$:$f'(2) = \frac{3}{5} - \frac{2}{5(2^2)} = \frac{3}{5} - \frac{2}{20} = \frac{3}{5} - \frac{1}{10}$$f'(2) = \frac{6 - 1}{10} = \frac{5}{10} = \frac{1}{2}$.

Let $3f(x) - 2f(1/x) = x,$ then $f'(2)$ is equal to

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