If \( f:(0, \infty) \rightarrow R \) be given by \( f(x)=\int_{1 / x}^{x} e^{-\left(t+\frac{1}{t... VIDEO
If \( f:(0, \infty) \rightarrow R \) be given by \( f(x)=\int_{1 / x}^{x} e^{-\left(t+\frac{1}{t}\right)} \frac{d t}{t} \).
Then,
[More than One Correct Option, 2014 Adv.]
(a) \( f(x) \) is monotonically increasing on \( [1, \infty) \)
(b) \( f(x) \) is monotonically decreasing on \( [0,1) \)
(c) \( f(x)+f\left(\frac{1}{x}\right)=0, \forall x \in(0, \infty) \)
(d) \( f\left(2^{x}\right) \) is an odd function of \( x \) on \( R \)
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