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

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Answer 1 · 2015-04-15T00:56:12

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.

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