Question

Inverse function question!???

Answer 1

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

Explanation:

`f(x)=√(x-2)+3 \implies x=\sqrt{f^(-1)(x)-2}+3 \\ \\ x-3=\sqrt{f^(-1)(x)-2} \\ \\ (x-3)^2=f^(-1)(x)-2 \\ \\ f^(-1)(x)=(x-3)^2+2`

Note we take the positive case because the domain of the original function is the same as the range of the inverse, and the domain of
`f(x)` is
`[2, \infty)`.