Let $f : \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbb{R}$ be given by
$$f(x) = (\log(\sec x + \tan x))^3$$
Then\\
(A) $f(x)$ is an odd function\\
(B) $f(x)$ is a one-one function\\
(C) $f(x)$ is an onto function\\
(D) $f(x)$ is an even function