Final answer:
The inverse of the function f(x) = (x-4)^(2)+2 is f^(-1)(x) = ±√(x - 2) + 4.
Step-by-step explanation:
The inverse of a function is found by switching the x and y variables and solving for y. To find the inverse of the function f(x) = (x-4)^(2)+2, we replace f(x) with y and switch x and y to get x = (y-4)^(2)+2. We then solve for y:
x = (y-4)^(2)+2
x - 2 = (y-4)^(2)
±√(x - 2) = y - 4
±√(x - 2) + 4 = y
Therefore, the inverse of f(x) is f^(-1)(x) = ±√(x - 2) + 4.