Question

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

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

Answer 1

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

$f\left(x\right)=\frac{\sqrt{x+3}}{x^2+3x+2}$

$x+3>0\Rightarrow x>-3\Rightarrow x\in (-3,\infty ).....\left(1\right)$

$x^2+3x+2\ne 0$

$x^2+x+2x+2\ne 0$

$(x+1)(x+2)\ne 0$

$x\ne -1,-2.....\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$, we have

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