Questions: If f(x) = x / (3x + 2), then the domain of f includes all real numbers except .

If f(x) = x / (3x + 2), then the domain of f includes all real numbers except .
Transcript text: If $f(x)=\frac{x}{3 x+2}$, then the domain of f includes all real numbers except $\square$ .
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Solution

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Solution Steps

Step 1: Identify the function and its domain

The function given is: \[ f(x) = \frac{x}{3x + 2} \] The domain of a rational function includes all real numbers except those that make the denominator zero.

Step 2: Find the value of \( x \) that makes the denominator zero

Set the denominator equal to zero and solve for \( x \): \[ 3x + 2 = 0 \] \[ 3x = -2 \] \[ x = -\frac{2}{3} \]

Step 3: Determine the domain

The domain of \( f(x) \) includes all real numbers except \( x = -\frac{2}{3} \).

Final Answer

\[ \boxed{x = -\frac{2}{3}} \]

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