What is the inverse of this function?

Question

Find the inverse of f(x)=(x-2)^2+1 algebraically.

Answer 1

let's use y to denote f(x)

so we have y=(x-2)^2+1 ===>>>. (y-1)=(x-2)^2

==>>>(y-1)^0.5=x-2 ==>>>>x=(y-1)^0.5+2

After finding this relation, let's switch y and x

we got y=(x-1)^0.5+2

the inverse function is thus f(x)=(x-1)^0.5+2