Question

Find the domain of following function:

$\sqrt{x^2-9}$

• A. $(-\infty ,-3]\cup [3,\infty )$
• B. $(-\infty ,-5)\cup (3,\infty )$
• C. $(-\infty ,-3)\cup (6,\infty )$
• D. None of these

Answer 1

The correct option is A $(-\infty ,-3]\cup [3,\infty )$

We have, $f\left(x\right)=\sqrt{x^2-9}$

We observe that $f\left(x\right)$ is defined for all $x$ satisfying

$x^2-9\ge 0$

$\Rightarrow (x-3)(x+3)\ge 0$

$\Rightarrow x\le -3$ or $x\ge 3$

$\Rightarrow x\in (-inf,-3]\cup [3,inf)$

Hence, $\text{D}$ is the correct option.