Question

The domain of the function $f$ given by $f\left(x\right)=\frac{x^2+2x+1}{x^2-x-6}$ is

• A. $R-\{3,-2\}$
• B. $R-\{3,2\}$
• C. $R-[-2,3]$
• D. $R-(-2,3)$

Answer 1

Answer: (A)

Given, $f\left(x\right)=\frac{x^2+2x+1}{x^2-x-6}$
For domain of $f\left(x\right)$, $x^2-x-6\ne 0$
$\therefore \left(x-3\right)\left(x+2\right)\ne 0$
$\Rightarrow x\ne 3,-2$
$\therefore$ Domain of $f\left(x\right)$ is $R-\left\{3,-2\right\}$.