Question

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

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

Answer 1

The correct option is D

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

Explanation for the correct option :

Find the domain of $F\left(x\right)$

Consider the given function as,

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

Define the above function as,

$$\begin{gathered} \Rightarrow x^2+3x+2\ne 0 \\ \Rightarrow \left(x+1\right)\left(x+2\right)\ne 0 \\ \Rightarrow x\ne -1,-2 \end{gathered}$$

Then,

$$\begin{gathered} \Rightarrow x+3>0 \\ \Rightarrow x>-3 \end{gathered}$$

Since, the domain of $F\left(x\right)$ is $\left(-3,\infty \right)-\left\{-1,-2\right\}$

Hence, the correct answer is Option D.