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. (d)

Solution:

  1. 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 $(-3, \infty) /{-1,-2}$



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