Question 388667
Assuming that {{{g(x)=-3x^3-6}}}, first replace g(x) with y to get {{{y=-3x^3-6}}}. Now swap x and y to get {{{x=-3y^3-6}}}



Now solve for y to get 



{{{x=-3y^3-6}}}



{{{x+6=-3y^3}}}



{{{-(x+6)/3=y^3}}}



{{{y=root(3,-(x+6)/3)}}}



So the inverse is {{{g^(-1)(x)=root(3,-(x+6)/3)}}}



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