The domain of the function f given by f(x)= x^2+2x+1 x^2-x-6 . - Vidyadip

MCQ

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

✓
$R – \{3, –2\}$
B
$R – \{–3, 2\}$
C
$R – [3, –2]$
D
$R – (3, –2)$

✓

Answer

Correct option: A.

$R – \{3, –2\}$

Given that: $\text{f(x)}=\frac{\text{x}^2+2\text{x}+1}{\text{x}^2-\text{x}-6}$
$f(x)$ is defined if $\text{x}^2-\text{x}-6\neq0$
$\Rightarrow\text{x}^2-3\text{x}+2\text{x}-6\neq0$
$\Rightarrow(\text{x}-3)(\text{x}+2)\neq0$
$\Rightarrow\text{x}\neq-2,\text{x}\neq3$
So, the domain of $f(x) = R - \{-2, 3\}$

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