Question

The domain of $f\left(x\right)=\frac{x^2-5x-16}{x^2-x-6}$ is

• A. $R-\{2,3\}$
• B. $R-\{-2,-3\}$
• C. $R-\{-2,3\}$
• D. $R-\{2,-3\}$

Answer 1

The correct option is C $R-\{-2,3\}$

$x^2-x-6\ne 0$
$\Rightarrow x^2-3x+2x-6\ne 0$
$x(x-3)+2(x-3)\ne 0$
$\Rightarrow x\ne -2,3$
$\therefore$ domain of $f$ is $R-$$\{-2,3\}$.