The range of $f\mathit{\left(}x\mathit{\right)}\mathit{=}\mathit{-}{x}^{\mathit{3}}\mathit{+}{x}^{\mathit{2}}\mathit{-}x\mathit{+}{\mathit{c}\mathit{o}\mathit{s}}^{\mathit{-}\mathit{1}}\mathit{ }x$ is

$\mathrm{f}\left(\mathrm{x}\right)=-{\mathrm{x}}^3+{\mathrm{x}}^2-\mathrm{x}+{\cos }^{-1} \mathrm{x}$

$$\begin{gathered} \mathrm{Domain} of f\left(x\right)=[-1,1] \\ {\mathrm{f}}^{\mathrm{\text{'}}}\left(\mathrm{x}\right)=-3{\mathrm{x}}^2+2\mathrm{x}-1-\frac{1}{\sqrt{1-{\mathrm{x}}^2}}<0 \end{gathered}$$

'f ' is a decreasing function

 $\therefore$ Min of f (x) is $\mathrm{f}\left(1\right)=-1+1-1+0=-1$

Max of f (x) is $\mathrm{f}(-1)=1+1+1+\mathrm{\pi }=3+\mathrm{\pi }$

Range$=\left[-1,3+\mathrm{\pi }\right]$