Given:
[tex]3y^3-4[/tex]This expression can be written as follows.
Cube the variable, multiply by 3, and then subtract 4.
Take the given expression as x as follows to find the inverse.
[tex]3y^3-4=x[/tex]Adding 4 on both sides of the equation, we get
[tex]3y^3-4+4=x+4[/tex][tex]3y^3=x+4[/tex]Dividing both sides by 3, we get
[tex]\frac{3y^3}{3}=\frac{x+4}{3}[/tex][tex]y^3=\frac{x+4}{3}[/tex]Taking cube root on both sides, we get
[tex]y=\sqrt[3]{\frac{x+4}{3}}[/tex]Hence the inverse expression is
[tex]\sqrt[3]{\frac{x+4}{3}}[/tex]This can be written as follows.
Add 4, divide by 3 and then take the cube root of the variables.