Let $f:(0,1) \rightarrow R$ be a function defined by $f(x)=\frac{1}{1-e^{-x}}$ and $g(x)=(f(-x)-f(x))$. Consider two statements (I) $g$ is an increasing function in $(0,1)$ (II) $g$ is one-one in $(0,1)$ Then, [JEE Main 2023, 25 Jan (Shift 1)]

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Let \(f:(0,1) \rightarrow R\) be a function defined by \(f(x)=\frac{1}{1-e^{-x}}\) and \(g(x)=(f(-x)-f(x))\). Consider t…

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