Question 60238
f(x) = (x+2)^3 - 8

Let y = (x+2)^3 - 8
To find the inverse first we interchange x and y and then solve for y.

So the given equation becomes..
x = (y+2)^3 - 8
==> x + 8 = (y+2)^3 - 8 + 8 [adding 8 to both the sides of the equality]
==> x + 8 = (y+2)^3
Taking cube root on both the sides,
(x + 8)^(1/3) = y+2
==> (x + 8)^(1/3)- 2 = y + 2 - 2 {adding -2 to both the sides]
==> (x + 8)^(1/3) - 2 = y 

Thus the inverse of the given function is given by..

f^(-1)(x) = (x + 8)^(1/3)-2

Good Luck!!!