The domain of the function f(x) = `(|x+3|)/(x + 3)` is

Options

A. {-3}
B. R - {-3}
C. R - {3)
D. R

Answer

To find the domain of the function \( f(x) = \frac{|x+3|}{x+3} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the components of the function**: The function consists of a numerator \( |x + 3| \) and a denominator \( x + 3 \).

2. **Determine when the denominator is zero**: For the function to be defined, the denominator cannot be zero. Therefore, we set:
\[ x + 3 \neq 0 \]

3. **Solve for \( x \)**: From the inequality above, we can solve for \( x \):
\[ x \neq -3 \]

4. **State the domain**: The domain of the function includes all real numbers except \( -3 \). In interval notation, this can be expressed as:
\[ \text{Domain} = (-\infty, -3) \cup (-3, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{|x+3|}{x+3} \) is \( (-\infty, -3) \cup (-3, \infty) \).

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