I'm assuming ya mean
[tex]y=\sqrt{x+6}-7[/tex]
alrighty, domain is the numbers you can use for x without making wierd stuf happen
the only numbers you can't use are the ones that cause a division by 0 or a squaer root of a negative number
no value of x will make a division by 0 but we can have a negative squaer root
solve for where it will be negative and restrict that reigon
the part under the squaer root is x+6
so
x+6<0
minus 6 both sides
x<-6
that is where we begin to see negative squaer roots
so the domain is x≥-6
