Question

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

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

Answer 1

The correct option is D (-3, $\infty$) - {-1, -2}

We have, $F\left(x\right)=\frac{lo{g}_2(x+3)}{x^2+3x+2}$
$\therefore$ F (x) is defined if x + 3 > 0 and $x^2$ + 3x + 2 $\ne$ 0
$\Rightarrow$ F(x) is defined if x > -3 and x $\ne$ -1, -2
$\Rightarrow$ Domain of F(x) = (-3, \infty) - {-1, -2}