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

Let \(f:(0,1) \rightarrow \mathrm{R}\) be a function defined by \(f(x)=\frac{1}{1-e^{-x}}\) and \(g(x)=(f(-x)-f(x))\).
Assertion (A): \(g\) is an increasing function in \((0,1)\)
Reason (R): \(g\) is one-one in \((0,1)\)
Then,

[JEE Main 2023, 25 Jan (Shift 1)]