Question

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

Answer 1

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

So we solve `"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,
`RR`
`(-oo, oo)`
or however your class is writing the answer.