I’ve just started learning inverse functions (I’m not behind, am I?!) and I don’t really understand how to find the domain and range of an inverse so could somebody please explain it to me?

So for example...

For the following function find the inverse and state it’s domain and range

f:[-2,0] —> R, f(x) = 2x - 4

So, I found that the inverse is...

f^-1 (x) = 1/2 (x+4)

I’m just not sure how to find the domain and range.