Surface defined on the domain?

"Let S be the surface z = e^(x+y) - 2, defined on the domain D = {(x,y) ∈ ℝ^2 | x ≥ 0 and y ≥ 0}. What is the minimal value of z for points on S?"

With this question, I thought that since both the x- and y-values need to be greater than zero for the domain, then obtaining the minimal value would simply mean subbing 0 into the equation. I did that, and got the answer, -1. (Which also matches up as being the correct answer to the question). So, I just basically want to know was what I did to get the answer correct or is there some other way you get the answer? (As, I may be wrong but it just seems that it was a bit of a straightforward and simple approach with getting the answer.)