Final answer:
The inverse function of f(x) = 2(x+3)^3 is f^{-1}(x) = (x/2)^(1/3) - 3.
Step-by-step explanation:
The inverse of a function can be found by switching the roles of x and y in the original function and solving for y.
To find the inverse of f(x) = 2(x+3)^3, we first switch x and y to get x = 2(y+3)^3.
Then, solve for y by taking the cube root of both sides and rearranging the equation:
x = 2(y+3)^3
(x/2) = (y+3)^3
y+3 = (x/2)^(1/3)
y = (x/2)^(1/3) - 3
Therefore, the inverse function of f(x) = 2(x+3)^3 is:
f^{-1}(x) = (x/2)^(1/3) - 3.