Question

The domain of the function $f\left(x\right)=\frac{{\log }_2(x+3)}{x^2+3x+2}$ 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)

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

Given function is $f\left(x\right)=\frac{{\log }_2(x+3)}{x^2+3x+2}$
Here, for existence of log
$x+3>0\Rightarrow x>-3$
$\Rightarrow xϵ(-3,\infty )$
and for existence of $f\left(x\right)$,
$x^2+3x+2\ne 0$
$\Rightarrow (x+1)(x+2)\ne 0$
$\Rightarrow x\ne -1,-2$
Hence, required domain of $f\left(x\right)$ is
$(-3,\infty )-\{-1,-2\}$.