\( f:[0, \infty) \rightarrow R \) be a function satisfying \( f(x) e^{f(x)}=x \forall x \in[0, \...
\( f:[0, \infty) \rightarrow R \) be a function satisfying \( f(x) e^{f(x)}=x \forall x \in[0, \infty) \), then which of the following statements is(are) TRUE?
(a) \( f^{\prime}(x) \geq 0 \forall x \in(0, \infty) \)
(b) \( \lim _{x \rightarrow \infty} f(x)=0 \)
(c) \( \lim _{x \rightarrow \infty} \frac{f(x)}{\ln x}=1 \)
(d) \( \lim _{x \rightarrow \infty} \frac{f(x)}{\ln x}=0 \)
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