Question 166272
{{{y=(3x+7)^3-5}}} Start with the given equation



{{{x=(3y+7)^3-5}}} Switch 'x' and 'y'. The goal now is to solve for 'y'



{{{x+5=(3y+7)^3}}} Add 5 to both sides.



{{{root(3,x+5)=3y+7}}} Take the cube root of both sides to eliminate the exponent of '3'



{{{3y+7=root(3,x+5)}}} Rearrange the equation



{{{3y=root(3,x+5)-7}}} Subtract 7 from both sides



{{{y=(root(3,x+5)-7)/3}}} Divide both sides by 3 to isolate (ie solve for) 'y'



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