Question

18. Identify the inverse function of

Answer 1

`\huge\boxed{D) \ f^(-1)(x) = (x-3)^2+2}`

Explanation:

`f(x) = √(x-2) + 3`

Replace f(x) by y

`y = √(x-2) + 3`

Interchange x and y

`x = √(y-2) + 3`

Solve for y

`x = √(y-2) + 3`

Subtracting 3 to both sides

`x - 3 = √(y-2)`

Taking square on both sides

`(x-3)^2 = y-2`

Adding 2 to both sides

`y = (x-3)^2 + 2`

Replace
`y = f^(-1)(x)`

`f^(-1)(x) = (x-3)^2+2`