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If $f(x)=4 x^3+3 x^2+3 x+4$, then $x^3 f\left(\frac{1}{x}\right)$ is
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$f(x)$
$\begin{aligned} x^3 f\left(\frac{1}{x}\right)= & x^3\left[\frac{4}{x^3}+\frac{3}{x^2}+\frac{3}{x}+4\right] \\ & =4+3 x+3 x^2+4 x^3=f(x)\end{aligned}$
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