First slide

Functions (XII)

Question

$The domain of definition of f (x) = \frac{\log_{2} (x + 3)}{x^{2} + 3 x + 2} is$

Moderate

A

$R - {- 1, - 2}$
B

$(- 2, \infty)$
C

$R - {- 1, - 2, - 3}$
D

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

Solution

$f (x) = \frac{\log_{2} (x + 3)}{x^{2} + 3 x + 2} \log_{2} (x + 3) \Rightarrow (x + 3) > 0 \Rightarrow x > - 3 \Rightarrow x \in (- 3, \infty) x^{2} + 3 x + 2 \neq 0 \Rightarrow (x + 1) (x + 2) \neq 0 \Rightarrow x \neq - 1, x \neq - 2 D o m a i n i s (- 3, \infty) - {- 1, - 2}$

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