If \( f(x)=x+\frac{1}{x} \), prove that :
\[
[f(x)]^{3}=f\left(x^{3}\right)+3 f\left(\frac{1}{x}...
If \( f(x)=x+\frac{1}{x} \), prove that :
\[
[f(x)]^{3}=f\left(x^{3}\right)+3 f\left(\frac{1}{x}\right) .
\]
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