Questions: Determine the domain of the function. f(x) = (4x - 7) / (4x + 44)

Determine the domain of the function. f(x) = (4x - 7) / (4x + 44)
Transcript text: Determine the domain of the function. \[ f(x)=\frac{4 x-7}{4 x+44} \]
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Solution

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Solution Steps

To determine the domain of the function \( f(x) = \frac{4x-7}{4x+44} \), we need to find the values of \( x \) for which the function is defined. The function is undefined when the denominator is zero. Therefore, we need to solve the equation \( 4x + 44 = 0 \) to find the values of \( x \) that are not in the domain.

Step 1: Identify the Function

We are given the function \( f(x) = \frac{4x - 7}{4x + 44} \).

Step 2: Determine When the Function is Undefined

The function is undefined when the denominator is equal to zero. We set the denominator equal to zero: \[ 4x + 44 = 0 \]

Step 3: Solve for \( x \)

To find the value of \( x \) that makes the denominator zero, we solve the equation: \[ 4x = -44 \implies x = -11 \]

Step 4: State the Domain

The domain of the function is all real numbers except for the value where the function is undefined. Therefore, the domain can be expressed as: \[ \text{Domain} = \mathbb{R} \setminus \{-11\} \]

Final Answer

The domain of the function is \\(\boxed{\mathbb{R} \setminus \{-11\}}\\).

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