What is the domain of the function $y=\sqrt{x+6}-7$ ? $x \geq-7$ $x \geq-6$ $x \geq 6$ $x \geq 7$

Step 1 ：The problem is asking for the domain of the function \(y=\sqrt{x+6}-7\).

Step 2 ：The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function.

Step 3 ：For a square root function, the value inside the square root (the radicand) must be greater than or equal to zero, because we cannot take the square root of a negative number in the real number system.

Step 4 ：In this case, the radicand is \(x+6\). So, we need to find the values of \(x\) for which \(x+6 \geq 0\).

Step 5 ：Solving the inequality \(x+6 \geq 0\) gives \(x \geq -6\).

Step 6 ：This means that the domain of the function \(y=\sqrt{x+6}-7\) is all real numbers greater than or equal to -6.

Step 7 ：\(\boxed{x \geq -6}\) is the final answer.