Question

The domain of the function $f \left(x\right)=\frac{\log_{2}\left(x+3\right)}{x^{2}+3x+2}$ is

• A. $R - \{ -1,-2 \}$
• B. $R -\{ -1,-2 ,0 \}$
• C. $(-3 ,-1)$ $\cup$ $(-1, \infty)$
• D. $(-3, \infty) - \{-1,-2\}$
• E. $(0,\infty)$

Answer 1

Answer: (D)

Given function is $f(x)=\frac{\log _{2}(x+3)}{x^{2}+3 x+2}$
Here, for existence of log
$x+3>\,0$
$ \Rightarrow x >\, -3$
$\Rightarrow \, x \in(-3, \infty)$
and for existence of $f(x)$,
$ x^{2}+3 x+ 2 \, \neq 0 $
$\Rightarrow \,(x+1)(x+2) \neq 0 $
$\Rightarrow \, x \neq-1,-2$
Hence, required domain of $f(x)$ is
$(-3, \infty)-\{-1,-2\}$