Question

Find the domain of the given function. f(x) = square root of quantity x plus six divided by quantity x plus seven times quantity x minus nine.

Answer 1

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