Answer:
If the function is [tex]y=\sqrt{x+6} -7[/tex] , the domain are all values of x greater than or equal to -6
If the function is [tex]y=\sqrt{x+6-7}[/tex] , the domain are all values of x greater than or equal to 1
Step-by-step explanation:
First case
we have
[tex]y=\sqrt{x+6} -7[/tex]
we know that
The radicand of the function must be greater than or equal to zero
so
[tex]x+6 \geq 0[/tex]
[tex]x\geq-6[/tex]
the solution is the interval---------> [-6,∞)
therefore
The domain are all values of x greater than or equal to -6
Second case
we have
[tex]y=\sqrt{x+6-7}[/tex]
so
[tex]y=\sqrt{x-1}[/tex]
we know that
The radicand of the function must be greater than or equal to zero
so
[tex]x-1 \geq 0[/tex]
[tex]x\geq 1[/tex]
the solution is the interval---------> [1,∞)
therefore
The domain are all values of x greater than or equal 1
