Answer
$[2,7)$
Work Step by Step
Let $f(x)=\sqrt {x-2}$ and $g(x)=\dfrac{1}{\sqrt{7-x}}$
In order to find the domain we will have to set the equation inside the square root greater than and equal to zero.
we have, $\sqrt {x-2} \geq 0$ and $\sqrt{7-x} \geq 0$
or, $x-2 \geq 0$ and $(\sqrt{7-x})^2 \geq (0)^2$
or, $x \geq 2$ and $7-x \geq 0$
or, $x \geq 2$ and $x \lt 7$
Thus, Domain for $\dfrac{f(x)}{g(x)}$ will be a set of interval to both domains, that is, $[2,7)$
