Question

List the operations being applied and the order in which they are applied to the variable. Choose the correct answer below.

Answer 1

Given:

$3y^3-4$

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.

$3y^3-4=x$

Adding 4 on both sides of the equation, we get

$3y^3-4+4=x+4$

$3y^3=x+4$

Dividing both sides by 3, we get

$\frac{3y^3}{3}=\frac{x+4}{3}$

$y^3=\frac{x+4}{3}$

Taking cube root on both sides, we get

$y=\sqrt[3]{\frac{x+4}{3}}$

Hence the inverse expression is

$\sqrt[3]{\frac{x+4}{3}}$

This can be written as follows.

Add 4, divide by 3 and then take the cube root of the variables.