Find \( f(2) \)
If
\[ 2f(x)-3f\left(\frac1x\right)=x^2 \qquad (x\ne0) \]
then \( f(2) \) is equal to
(a) \(-\frac74\)
(b) \(\frac52\)
(c) \(-1\)
(d) none of these
Replace \(x\) by \(\frac1x\),
\[ 2f\left(\frac1x\right)-3f(x)=\frac1{x^2} \]
Given,
\[ 2f(x)-3f\left(\frac1x\right)=x^2 \]
Solving,
\[ -5f(x)=\frac3{x^2}+2x^2 \]
\[ f(x)=-\frac15\left(\frac3{x^2}+2x^2\right) \]
Put \(x=2\),
\[ f(2) = -\frac15\left(\frac34+8\right) \]
\[ = -\frac{35}{20} = -\frac74 \]
\[ \boxed{\text{Correct Answer: (a)}} \]