Question

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

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

Answer 1

Answer: (D)

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

$f\left(x\right)=\frac{{\log }_2(x+3)}{(x+1)(x+2)}$

Hence for domain of $f\left(x\right)$

$x+3>0$

$x>-3$
Also, Denominator cannot be zero.

So, $x\ne -1$ and $x\ne -2$

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