If \( f(x)=8 x^{3}+3 x \), then \( \lim _{x \rightarrow \infty} \frac{f^{-1}(8 x)-f^{-1}(x)}{x^{...

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If \( f(x)=8 x^{3}+3 x \), then \( \lim _{x \rightarrow \infty} \frac{f^{-1}(8 x)-f^{-1}(x)}{x^{1 / 3}} \) is
(a) \( \frac{1}{2} \)
(b) \( 2 \frac{1}{3} \)
(c) \( \frac{2^{1 / 3}-1}{2} \)
(d) \( \frac{1}{4} \)
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