Question

Find the domain of $h\left(x\right)=\frac{1}{\sqrt{(}|-x^2-9|)}$

Answer 1

Start with the given function $h\left(x\right)=\frac{1}{\sqrt{{|-x}^2-9|}}$
Set the denominator equal to zero. Remember, dividing by $0$ is undefined. So if we find values of $x$ that make the denominator zero, then we must exclude them from the domain.
$\sqrt{{|-x}^2-9|}=0$

$\Rightarrow$$x^2=-9$

If we find the roots of the above quadratic equation we get the imaginary values for $x$.
Since the imaginary value of $x$ makes the denominator equal to zero, this means
The domain is: $(-infinity,+infinity)$.