Mathematics

Problem

Let the function

g: (-\infty, \infty) \to \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

be given by

g(u) = 2 \tan^{-1}(e^u) - \frac{\pi}{2}.

Then,

g

is [2008] (a) even and is strictly increasing in

(0, \infty)

(b) odd and is strictly decreasing in

(-\infty, \infty)

(-\infty, \infty)

(d) neither even nor odd, but is strictly increasing in

(-\infty, \infty)