What is the domain of the function y equals the square root of x+6-7?

I am assuming that your function is
due to the fact you did not write x-1

the domain is the numbers you can use for x without getting wierd results
wierd results happen when you divide by 0 or take the square root of a negative number

the arean't any division signs so no division by 0
but there is a square root sign
so the part under the square root must be greater than or equal to 0
find where it is equal to 0
0=x+6
minus 6
-6=x
when x is smaller than -6, we get undefined because we get square root of a negative

so the domain (numbers you can use for x) is D={x|x≥-6} or basically x≥-6