Question

The domain of $f\left(x\right)=\frac{1}{\sqrt{x^2+2x+9}}$ is

• A. $(1,9)$
• B. $(1,2)$
• C. $(-\infty ,\infty )$
• D. $(0,\infty )$

Answer 1

The correct option is C $(-\infty ,\infty )$

For $g\left(x\right)=x^2+2x+9$, $a>0$
Hence for $g\left(x\right)>0$, $D<0$

$D=b^2-4ac=4-4\left(9\right)=-27<0.$
$\therefore$ $f$ is defined for all $x\in (-\infty ,\infty )$