What is the inverse of f(x)=(x-2)^3

g⁻¹(x) = 2 + ∛x

Step-by-step explanation:

g(x) = (x - 2)³     Rename g(x) as y

   y = (x - 2)³

Solve for x :

        y = (x - 2)³     Multiply each side by 3

     ∛y =  x - 2         Add 2 to each side

∛y + 2 = x  

        x = ∛y + 2      Switch x and y

        y = ∛x + 2      Rename y as g inverse

 g⁻¹(x) = 2 + ∛x

See the graphs of g(x) and g⁻¹(x) below.

g(x) is the red line. g⁻¹(x) is the blue line.

Each graph reflects the other about the dashed line representing the function y = x.