Question

The domain of $g\left(x\right)=\frac{1}{\sqrt{(}{x}^2+2x+6)}$ is $(-\infty ,0)$

Write 1 if true and 0 if flase

Answer 1

Start with the given function $g\left(x\right)=\frac{1}{\sqrt{x^2+2x+6}}$
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.
$\sqrt{x^2+2x+6}=0$

$\Rightarrow$$x^2+2x+6=0$

If we find the roots of the above quadratic equation we get the imaginary values for $x$.
The domain is: $(-\infty ,+\infty )$.