Question 366586
The idea is to first replace f(x) with y, and then swap x and y. From there, solve for y to find the inverse function. So...


{{{f(x)=(6x-7)^3+5}}}



{{{y=(6x-7)^3+5}}}



{{{x=(6y-7)^3+5}}}



{{{x-5=(6y-7)^3}}}



{{{root(3,x-5)=6y-7}}}



{{{root(3,x-5)+7=6y}}}



{{{(1/6)(root(3,x-5)+7)=y}}}



{{{y=(1/6)(root(3,x-5)+7)}}}



This means that the inverse function is *[Tex \LARGE f^{-1}(x)=\frac{1}{6}\left(\sqrt[3]{x-5}+7\right)]