11.2#10

Hi Dr. Taylor,

I solved this question with a math tutor, and we weren't positive why the answer was choice B, I feel choice E should be the answer since one could write f(x,y) as ((inf-n, inf - n - 1)) such that the values
can be massive or equal to each other and allowed in the domain?

Any feedback regarding a proof for B being the answer would be appreciated.

Thanks,

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Well, the point is that you need the arguments of both square roots to be non-negative. For the first square root this means that x + y ≥ 0 or equivalently y ≥ -x. For the second square root this means that x - y ≥ 0  or x ≥ y.  If you just put these together you get x ≥ y ≥ -x.   Notice that this implies that
x ≥ -x; this means that x ≥ 0 (because if x < 0 , -x is positive so x ≥ -x is not true ), so the domain is the wedge between the lines y = x and y = -x with x ≥ 0: