Question 253595
Let {{{y=4-3x^3}}}



{{{y=4-3x^3}}} Start with the given equation.



{{{x=4-3y^3}}} Swap x and y 



{{{x-4=-3y^3}}} Subtract 4 from both sides.



{{{(x-4)/(-3)=y^3}}} Divide both sides by -3.



{{{-(x-4)/(3)=y^3}}} Reduce



{{{root(3,-(x-4)/(3))=y}}} Take the cube root of both sides to isolate y



{{{y=root(3,-(x-4)/(3))}}} Rearrange the terms.



So the inverse function is *[Tex \LARGE f^{-1}(x)=\sqrt[3]{-\frac{x-4}{3}}]