Choose the correct answers: The domain of the function f given by… - Vidyadip

MCQ

Choose the correct answers: 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}

R – {3, –2}

Solution:
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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