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.