What is the inverse of this equation?

Inverting a function is equivalent to solve the equation x = f(y) for the variable y.

Take the function:

y = ∛(x – 2) + 6

Switch x and y, and then solve the equation for y:

x = ∛(y – 2) + 6

x – 6 = ∛(y – 2)

∛(y – 2) = x – 6

Cube both sides:

[ ∛(y – 2) ]³ = (x – 6)³

y – 2 = (x – 6)³

y = (x – 6)³ + 2    <———   and there it is, the inverse function.

I hope this helps. =)