The domain of the function f given by f x = 1 x 2 - x - 6 is
The domain of the function given by is
$(-\infty, -2) \cup [4, \infty)$
$(-\infty, -2) \cup (4, \infty)$
Solution
Given that $f(x) = \frac{1}{\sqrt{x^2 - x - 6}}$,
$f$ is defined if $x^2 - x - 6 > 0$ or $|x - 3| |x + 2| > 0$,
$\Rightarrow x < -2$ or $x > 3$, $\Rightarrow x < -2$ or $x \geq 4$.
Hence, domain $= (-\infty, -2) \cup [4, \infty)$.