If $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\sin \mathrm{x},\mathrm{g}\left(\mathrm{x}\right)={\mathrm{e}}^{-\mathrm{x}},\mathrm{u}=\sqrt{\mathrm{c}+1}-\sqrt{\mathrm{c}},$$\mathrm{v}=\sqrt{\mathrm{c}}-\sqrt{\mathrm{c}-1},(\mathrm{c}>1),$then

$$\begin{gathered} \mathrm{u}=\sqrt{\mathrm{c}+1}-\sqrt{\mathrm{c}} \\ \mathrm{u}=\frac{1}{\sqrt{\mathrm{c}+1}+\sqrt{\mathrm{c}}}\text{ and }\mathrm{v}=\frac{1}{\sqrt{\mathrm{c}-1}+\sqrt{\mathrm{c}}} \end{gathered}$$
Clearly, $\mathrm{u}<\mathrm{v}.$
Also, f is increasing whereas g is decreasing. Thus, 
      $\mathrm{u}<\mathrm{v}$
or $\mathrm{f}\left(\mathrm{u}\right)<\mathrm{f}\left(\mathrm{v}\right)$
or  $\mathrm{gof}\left(\mathrm{u}\right)>\mathrm{gof}\left(\mathrm{v}\right)$