A) contains more than two elements.
B) is an empty set.
C) contains exactly one element
D) contains exactly two elements
Correct Answer: D
Solution :
\[f(x)+2f(1/x)=3x\] .... (1) \[x\to \frac{1}{x}\Rightarrow f(1/x)+2f(x)=3/x\] ?(2) \[f(x)+2\left( \frac{3}{x}-2f(x) \right)=3x\] \[\Rightarrow 3f(x)=\frac{6}{x}-3x\] \[\Rightarrow f(x)=\frac{2}{x}-x\] For S \[f(x)=f(-x)\Rightarrow \frac{2}{x}-x=0\] \[\Rightarrow x=\pm \sqrt{2}\]
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