Question

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

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

Answer 1

The correct option is B $R–\{3,–2\}$

Given:$f\left(x\right)=\frac{x^2+2x+1}{x^2-x-6}$

$[\because \frac{f\left(x\right)}{g\left(x\right)}$ is defined when $g\left(x\right)\ne 0$ and

both f(x) and g(x) are also defined]

$\Rightarrow x^2-x-6\ne 0$

$\Rightarrow x^2-3x+2x-6\ne 0$

$\Rightarrow x(x-3)+2(x-3)\ne 0$

$\Rightarrow (x-3)(x+2)\ne 0$

$\Rightarrow x\ne 3,-2$

Domain of $f=R–\{3,-2\}$

Hence, option (A) is correct