Questions: Find the domain of the rational function. f(x)=3x/(x+3)

Find the domain of the rational function. f(x)=3x/(x+3)
Transcript text: Find the domain of the rational function. \[ f(x)=\frac{3 x}{x+3} \]
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Solution

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Solution Steps

To find the domain of the rational function \( f(x) = \frac{3x}{x+3} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator is zero. Therefore, we need to find the values of \( x \) that make the denominator zero and exclude them from the domain.

Step 1: Identify the Function

We are given the rational function \( f(x) = \frac{3x}{x+3} \).

Step 2: Determine When the Function is Undefined

The function is undefined when the denominator is equal to zero. We set the denominator \( x + 3 \) to zero and solve for \( x \): \[ x + 3 = 0 \implies x = -3 \]

Step 3: Define the Domain

The domain of the function consists of all real numbers except the value that makes the denominator zero. Therefore, the domain can be expressed as: \[ \text{Domain} = \mathbb{R} \setminus \{-3\} \]

Final Answer

The domain of the function is \\(\boxed{\mathbb{R} \setminus \{-3\}}\\).

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