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x+6>=0


x>= -6

we have

\(y=\sqrt{x+6} -7\)

we know that

The radicand  of the function must be greater than or equal to zero

so

\(x+6 \geq 0\)

\(x\geq-6\)

the solution is the interval---------> [-6,∞)

therefore

the answer is

The domain are all values of x  greater than or equal to minus six