# How do you find the domain of the rational function g(x)=(x+4)/(x^2+4)?

Apr 15, 2015

The domain of a rational function is the set of all real numbers for which the denominator is not $0$.

So we solve $\text{denominator} = 0$ and take those out of the set of real numbers, what's left is the domain.

${x}^{2} + 4 = 0$ requires

${x}^{2} = - 4$ which has no solution in the real numbers.

So the domain is all real numbers,
$\mathbb{R}$
$\left(- \infty , \infty\right)$