Question

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

• A. $( - 3,\infty)$
• B. $\{ - 1, - 2\}$
• C. $( - 3,\infty) - \{ - 1, - 2\}$
• D. $( - \infty,\infty)$

Answer 1

Answer: (C)

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

Answer 2

Here $f(x) = \frac{\log_{2}(x + 3)}{x^{2} + 3x + 2} = \frac{\log_{2}(x + 3)}{(x + 1)(x + 2)}$ exists if,

Numerator $x + 3 > 0 \Rightarrow x > - 3$ …... (i)

and denominator $(x + 1)(x + 2)$ ≠ 0 $\Rightarrow x \neq - 1, - 2$ …… (ii)

Thus, from (i) and (ii); we have domain of $f(x)$ is

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