Functions 1 Question 6
6. The domain of definition of $f(x)=\frac{\log _2(x+3)}{x^{2}+3 x+2}$ is
(2001, 1M)
(a) $R /{-1,-2}$
(b) $(-2, \infty)$
(c) $R /{-1,-2,-3}$
(d) $(-3, \infty) /{-1,-2}$
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Answer:
Correct Answer: 6. (c)
Solution:
- Given, $f(x)=\frac{\log _2(x+3)}{\left(x^{2}+3 x+2\right)}=\frac{\log _2(x+3)}{(x+1)(x+2)}$
For numerator, $x+3>0$
$\Rightarrow \quad x>-3$
and for denominator, $(x+1)(x+2) \neq 0$
$$ \Rightarrow \quad x \neq-1,-2 $$
From Eqs. (i) and (ii),
Domain is $(-3, \infty) /{-1,-2}$
