For this case we have the following function:
[tex] \sqrt{ \frac{x+6}{x + 7(x-9)}} [/tex]
Rewriting the function we have:
[tex] \sqrt{ \frac{x+6}{x + 7x - 63}} [/tex]
[tex] \sqrt{ \frac{x+6}{8x - 63}} [/tex]
Separating the roots we have:
[tex] \frac{ \sqrt{x+6} }{ \sqrt{[tex]8x-63 \ \textgreater \ 0
[/tex]}} [/tex]
Then, the domain of the function is given by:
[tex]x+6 \geq 0
x \geq -6 [/tex]
And:
[tex]8x \ \textgreater \ 63[/tex]
Answer:
[tex]x+6 \geq 0 x \geq -6 [/tex]
or
[tex]8x \ \textgreater \ 63[/tex]
