Final answer:
The inverse of f(x) = (x - 3)^3 + 2 is g(x) = ∛(x - 2) + 3.
Step-by-step explanation:
The inverse of the function f(x) = (x - 3)^3 + 2 can be found by swapping the x and y variables and solving for y. Let's call the inverse function g(x).
Step 1: Swap x and y to get x = (y - 3)^3 + 2.
Step 2: Solve the equation for y.
x - 2 = (y - 3)^3
∛(x - 2) = y - 3
y = ∛(x - 2) + 3.
Therefore, the inverse of f(x) = (x - 3)^3 + 2 is g(x) = ∛(x - 2) + 3.