Application of Derivatives

Let $$f:(0,1)\to\mathbb{R}$$ be a function defined $$f(x) = {1 \over {1 - {e^{ - x}}}}$$, and $$g(x) = \left( {f( - x) - f(x)} \right)$$. Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,