Please help!

I have the solutions to them, I am just trying to understand how they were reached.

Find the inverse of the given functions and find the domain for f(x) and f^-1(x)

so I understand that you just flip the x and y

but what does it mean domain?

heres a couple

f(x)=x-2 over x+1

I know dom f(x)= [-2, infinity) but how is dom f^-1(x) = x+2 over 1-x??

maybe that explanation will help me with the other ones

rational functions:

heres a couple, I understand how to do most of them but I get stuck at little aspects of it.

find domain, intercepts, and asymptotes when appropriate:

y=(x-2)^2 + 1

why is there no x intercept? I got it as being x= square root of 5

y= 1 over x-1 +2

(the 2 is separate from the fraction)

How is that =0 solved? for some reason I got x=0, I guess its because I don't know how to solve that equation since the x is in denominator. but the solution says x=1/2

Final is tomorrow:/

Thanks so much for all your help!