The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]
Domain of a function refers to the values or range of input values of a function for which the function exists in real.
In this problem the given function is
[tex]y=\sqrt{(x+6)}-7[/tex]
Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.
So, for existence of function it is must to
[tex]x+6\geq0[/tex]
[tex]x\geq-6[/tex]
Hence the domain of the given function is given by [tex]x\geq-6[/tex]
Hence the correct option is (B).
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