Find \( f(x) \)
If
\[ 3f(x)+5f\left(\frac1x\right)=\frac1x-3 \]
for all non-zero \(x\), then \(f(x)=\)
(a) \(\frac1{14}\left(\frac3x+5x-6\right)\)
(b) \(\frac1{14}\left(-\frac3x+5x-6\right)\)
(c) \(\frac1{14}\left(-\frac3x+5x+6\right)\)
(d) none of these
Replace \(x\) by \(\frac1x\),
\[ 3f\left(\frac1x\right)+5f(x)=x-3 \]
Given,
\[ 3f(x)+5f\left(\frac1x\right)=\frac1x-3 \]
Solving the equations,
\[ 14f(x)=5x-\frac3x-6 \]
Therefore,
\[ f(x)=\frac1{14}\left(-\frac3x+5x-6\right) \]
\[ \boxed{\text{Correct Answer: (b)}} \]