$f:R\to Risafunctiondefinedbyf\left(x\right)=\frac{e^{\left|x\right|}-e^{-x}}{e^x+e^{-x}}.Thenfis$

$\begin{array}{l}f\left(x\right)=\frac{e^{\left|x\right|}-e^{-x}}{e^x+e^{-x}}=\{\begin{array}{l}\frac{e^x-e^{-x}}{e^x+e^{-x}}ifx\ge 0\\ \frac{e^{-x}-e^{-x}}{e^x+e^{-x}}ifx<0\end{array}\\ =\{\begin{array}{l}\frac{e^x-e^{-x}}{e^x+e^{-x}}ifx\ge 0\\ 0ifx<0\end{array}\\ \forall x<0,f\left(x\right)=0\\ \therefore fisnotone-one\end{array}$

$\begin{array}{l}forx\ge 0,f\left(x\right)=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^x+e^{-x}-2e^{-x}}{e^x+e^{-x}}\\ =1-\frac{2e^{-x}}{e^x+e^{-x}}\\ =1-\frac{2}{e^{2x}+1}\\ Ifx\ge 0\Rightarrow e^{2x}\ge 1\\ \Rightarrow e^{2x}+1\ge 2\\ \Rightarrow 2\le e^{2x}+1<0\end{array}$

$\begin{array}{l}\Rightarrow \frac{1}{2}\ge \frac{1}{e^{2x}+1}>0\\ \Rightarrow 1\ge \frac{x}{e^{2x}+1}>0\\ \Rightarrow -1\le \frac{-2}{e^{2x}+1}<0\\ \Rightarrow 0\le 1-\frac{2}{e^{2x}+1}<1\\ \therefore Range=[0,1)\ne codomain\\ \therefore fisnotonto\end{array}$