Question

Find the domains of definition of the following functions.
$y=\frac{\sqrt{x+5}}{\log (9-x)}.$

Answer 1

$y=\frac{\sqrt{x+5}}{log(9-x)}$

For $y$ to be real and defined.

$x+5$ must be $\ge 0\Rightarrow x\ge -5$

$9-x$ must be $>0\Rightarrow x<9$

$log(9-x)\ne 0\Rightarrow x\ne 8$

Therefore,domain of $y$ is $x\in [-5,8)\cup (8,9).$