Mathematics - Functions Question with Solution | TestHub

$f(x)=-x^3+x^2-x+{\cos }^{-1}x$ $\begin{array}{rlr}& \text{ Domain }=[-1,\cdot ]& f^{\prime }(x)=-3x^2+2x-1-\frac{1}{\sqrt{1-x^2}}<0\end{array}$

' $f$ ' is a decreasing function

$\text{ ∴ Min of }f(x{)}_{\text{is }}f(1)=-1+1-1+0=-1$

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

Range $=[-1,3+\pi ]$