Let $$f: (0, \infty) \rightarrow R$$ be given by
$$f(x) = \int_{\frac{1}{x}}^{x} e^{-(t + \frac{1}{t})} \frac {dt}{t}.$$
Then

A

f(x) is monotonically increasing on $$[1, \infty)$$

B

f(x) is monotonically decreasing on (0, 1)

C

$$f(x) + f \left(\frac{1}{x}\right) = 0,$$ for all $$x \in (0, \infty)$$

D

$$f(2^x)$$ is an odd function of x on R