If $f: R \rightarrow R$ is a function defined by $f(x) = e^{|x|} - e^{-x}$ / $e^{x} + e^{-x}$, then $f$ is:\\
(1) bijective\\
(2) $f$ is monotonically increasing on $(0, \infty)$\\
(3) $f$ is monotonically decreasing on $(0, \infty)$\\
(4) not differentiable at $x = 0$