Let \( f \) be a polynomial function satisfying \( f\left(x^{2}\right)-x f(x) \) \( =x^{4}\left(...

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Let \( f \) be a polynomial function satisfying \( f\left(x^{2}\right)-x f(x) \) \( =x^{4}\left(x^{2}-1\right) \forall x \in R^{+} \), which of the following is correct?
(a) \( f \) is an even function
(b) \( f \) is an odd function
(c) \( \lim _{x \rightarrow \infty} \frac{f(x)}{x^{3}}=1 \)
(d) \( \lim _{x \rightarrow \infty}\left(\frac{f(x)}{x^{2}}-x\right) \) exists and is equal to a non-zero quantity
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