I'm guessing you're given the function [tex]y(x)=2-x^3[/tex], and you're asked to find the inverse function [tex]y^{-1}(x)[/tex]. To do this, swap [tex]x[/tex] and [tex]y[/tex], then solve for [tex]y[/tex]:
[tex]x=2-y^3\implies y^3=2-x\implies y=(2-x)^{1/3}=\sqrt[3]{2-x}[/tex]
so that the inverse function is
[tex]y^{-1}(x)=\sqrt[3]{2-x}[/tex]
Just to verify:
[tex]y(y^{-1}(x))=y(\sqrt[3]{2-x})=2-(\sqrt[3]{2-x})^3=2-(2-x)=x[/tex]
[tex]y^{-1}(y(x))=y^{-1}(2-x^3)=\sqrt[3]{2-(2-x^3)}=\sqrt[3]{x^3}=x[/tex]
But in case you're actually only interested in computing the square root, first we note that [tex]\sqrt x[/tex] (the real-valued square root) is only defined as long as [tex]x\ge0[/tex]. So [tex]\sqrt{-x^3}[/tex] is defined as long as [tex]-x^3\ge0[/tex], or [tex]x^3\le0[/tex], or equivalently [tex]x\le0[/tex]. Under this condition, we could write
[tex]\sqrt{-x^3}=\sqrt{-x\times x^2}=\sqrt{-x}\sqrt{x^2}[/tex]
We can simplify this further, but we have to be careful. Suppose [tex]x=-1[/tex]. Then [tex]x^2=(-1)^2=1[/tex]. But we get the same result if [tex]x=1[/tex], since [tex]x^2=1^2=1[/tex]. There are two possible values of [tex]x[/tex] that given the same value of [tex]x^2[/tex], so to capture both of them, we take [tex]\sqrt{x^2}=|x|[/tex], the absolute value of [tex]x[/tex]. Then
[tex]\sqrt{-x^3}=|x|\sqrt{-x}[/tex]
We can't simplify the square root term further than this.
