Answer
The domain of this function is all real numbers.
Work Step by Step
To find the domain of this function, we need to find which values are excluded for $x$. In a rational function, the denominator cannot equal $0$ because the function would be undefined. Therefore, we need to set the denominator equal to $0$ and solve for $x$:
$x^2 + 16 = 0$
Subtract $16$ from each side of the equation:
$x^2 = -16$
If we take the square root of both sides, we will end up with a non-real number. Therefore, there are no restrictions on $x$, and the domain of this function is all real numbers.
