Question

The domain of the function $f\left(x\right)=\frac{\left|x+3\right|}{\left(x+3\right)}$ is

• A. $\left\{-3\right\}$
• B. $R-\left\{-3\right\}$
• C. $R-\left\{3\right\}$
• D. $R$

Answer 1

The correct option is B

$R-\left\{-3\right\}$

Explanation for correct answer Option(s)

Find the domain of the function $f\left(x\right)$

Consider the given function as,

$f\left(x\right)=\frac{\left|x+3\right|}{\left(x+3\right)}$

Defined the above function for all real values of $x$ for which,

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

Hence, the domain of the function is $R-\left\{-3\right\}$

Therefore, the correct answer is Option B.