Question

To ensure the inverse of domain of f. What is the f(x)=(x-4)^(2)+2

Answer 1

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.