A) \[2/7\]
B) \[1/2\]
C) 2
D) \[7/2\]
Correct Answer: B
Solution :
\[3f(x)-2f(1/x)=x\] .....(i) Let \[1/x=y\], then \[3f(1/y)-2f(y)=1/y\] Þ \[-2f(y)+3f(1/y)=1/y\] Þ \[-2f(x)+3f(1/x)=1/x\] .....(ii) From 3 × (i) + 2 × (ii), \[9f(x)-6f(1/x)-4f(x)+6f(1/x)=3x+2/x\] \[5f(x)=3x+\frac{2}{x}\] Þ \[f(x)=\frac{1}{5}\left[ 3x+\frac{2}{x} \right]\] Þ \[f'(x)=\frac{1}{5}\left[ 3-\frac{2}{{{x}^{2}}} \right]\]Þ \[{f}'(2)=\frac{1}{5}\left[ 3-\frac{2}{4} \right]=\frac{1}{2}\].
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