If $f\left(x\right)=|x+1|-2|x-1|$ then

If graph of $y=f\left(x\right)$ is as shown in figure

then which of the following option is correct?

Let $f$ be a real-valued function defined by $\mathrm{f}\left(\mathrm{x}\right)=\frac{{\mathrm{e}}^{\mathrm{x}}-{\mathrm{e}}^{-\left|\mathrm{x}\right|}}{{\mathrm{e}}^{\mathrm{x}}+{\mathrm{e}}^{-\left|\mathrm{x}\right|}},$ then the range of $f\left(x\right)$ is