Answer:
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.
