Final answer:
The inverse of the function Y=(X-4)^3 is found by swapping X and Y and solving for Y, resulting in the inverse function Y=∛X + 4.
Step-by-step explanation:
To find the inverse of the function Y=(X-4)^3, we need to swap the roles of 'X' and 'Y' and then solve for 'Y'. Starting with Y=(X-4)^3, we swap to X=(Y-4)^3. Next, we take the cube root of both sides to get ∛X=Y-4. Finally, we solve for 'Y' by adding 4 to both sides resulting in Y=∛X + 4. The inverse function is therefore Y=∛X + 4, where '∛' denotes the cube root.