## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

The domain of $H(x)$ is the set of all real numbers.
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 $0$ $\text{Setting the denominator equal to zero}$ $$x^2+4=0\\[3mm]\\ x^2=-4 \\ \text{ This has no real roots because when a real number is squared, the result is never a negative number.}$$ Thus, the domain of $H(x)$ is the set of all real numbers.