#### Answer

The domain of $G(x)$ is the set of all real numbers.

#### Work Step by Step

Rational functions are of the form
$$R(x)=\dfrac{p(x)}{q(x)}$$
The domain of the rational function is the set of all real numbers except those for which the denominator $q(x)$ is $0$.
$\text{Set the denominator equal to zero then solve:}$
$$x^4+1=0\\
x^4=-1\\
\text{ This equation has no real roots because any real number raised} \\\text{ to the fourth power will never
be negative.}$$
Thus, the domain of $G(x)$ is the set of all real numbers.