The initial function is:
[tex]y=\sqrt[]{x-3}-9[/tex]So the domain will be all values that made the root positive so:
[tex]\begin{gathered} x-3=0 \\ x=3 \end{gathered}[/tex]So the domain will be:
[tex]\text{domain}\to\mleft\lbrack3,\infty\mright)[/tex]So are all the numbers greater than or equal to 3
