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

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.

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 \(49 - x^2\).

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

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