what is the inverse function of of x^3 -2?

Answer 1

If y = x^3 - 2, then

x = (y+2)^(1/3)

Answer 2

Let y = x³ -2
Solve for x:
y+2 = x³
x = (y+2) ^ 1/3.
Now swap x and y.
y = (x+2)^(1/3).
That's how you find inverse functions in general.

Answer 3

The inverse of a function y=f(x) is a function g=f^(-1) (y) such that

g(f(x)) = x.

Thus, you just need to add 2 and apply the cubical root.

So the answer is
g(x) = 3d-degree-root (x+2).