Questions: The domain of (f ∘ g)(x) in interval notation is.

The domain of (f ∘ g)(x) in interval notation is.
Transcript text: The domain of $(f \circ g)(x)$ in interval notation is.
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Solution

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Solution Steps

To find the domain of the function \((f \circ g)(x) = \frac{13}{49 - x^2}\), we need to determine the values of \(x\) for which the denominator is not zero. This involves solving the equation \(49 - x^2 \neq 0\) and finding the intervals where this inequality holds.

Step 1: Identify the Denominator

To find the domain of the function \((f \circ g)(x) = \frac{13}{49 - x^2}\), we need to ensure that the denominator is not zero. The denominator is \(49 - x^2\).

Step 2: Solve for Zero Denominator

Set the denominator equal to zero and solve for \(x\): \[ 49 - x^2 = 0 \] \[ x^2 = 49 \] \[ x = \pm 7 \]

Step 3: Determine the Domain

The function \((f \circ g)(x)\) is undefined at \(x = 7\) and \(x = -7\). Therefore, the domain of \((f \circ g)(x)\) is all real numbers except \(x = 7\) and \(x = -7\).

Final Answer

\[ \boxed{(-\infty, -7) \cup (-7, 7) \cup (7, \infty)} \]

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