If f is a real function, find the domain of
`f(x)=(1)/(3x+2)`

Answer

To find the domain of the function \( f(x) = \frac{1}{3x + 2} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the function**: We have the function \( f(x) = \frac{1}{3x + 2} \).

2. **Determine when the function is undefined**: A rational function is undefined when its denominator is equal to zero. Therefore, we need to set the denominator \( 3x + 2 \) equal to zero and solve for \( x \):
\[ 3x + 2 = 0 \]

3. **Solve for \( x \)**:
\[ 3x = -2 \]
\[ x = -\frac{2}{3} \]

4. **State the domain**: The function \( f(x) \) is defined for all real numbers except for the value we found. Thus, the domain of \( f(x) \) can be expressed in interval notation as:
\[ \text{Domain} = (-\infty, -\frac{2}{3}) \cup (-\frac{2}{3}, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{1}{3x + 2} \) is \( (-\infty, -\frac{2}{3}) \cup (-\frac{2}{3}, \infty) \).

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