If \(\rm f(x)=2\left(\tan ^{-1}\left(e^{x}\right)-\frac{\pi}{4}\right)\), then f(x) is :
1
even and is strictly increasing in (0, ∞)
2
even and is strictly decreasing in (0, ∞)
3
odd and is strictly increasing in (–∞, ∞)
4
odd and is strictly decreasing in (–∞, ∞)