the direction was to find f^(-1)x.

Question

f(x) = x^2+2x+1, x >= -1

as a final answer, I got:
f^(-1)x = sqrt(x) - 1, x >= 0

is this right? I don't understand the restriction rules.

It is right. If originally x>=-1, that puts f(x) >=0, and in the inverse function, this restriction travels to the new domain.

kristie, Bob is correct. The restriction rule carries to f-inv.
In general, even funcions, those with a poly. whose degree is an even integer, must be restricted. They are not 1-1. 1-1 means that each horizontal line through f(x) intersects f in at most one point.
Note that restricting f here makes it 1-1, thus invertible.