What is the domain of $f (x) = \frac{x + 6}{x^{2} + 5}$ $f(x)=(x+6)/(x^2+5)$ ?

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Answer 1 · 2015-09-07T12:56:23

The domain of the function is $RR$ .

The domain of a function is the set of numbers for which that function is defined.

For simple rational functions, the only points where the function is undefined are when the denominator equals $0$ .

Thus, the domain is the set of all real numbers except the solutions to $x^2 + 5 = 0$ .

However, if you try to solve that quadratic equation, you'll notice that that equation has no real solutions.

$x^2 + 5 = 0$
$x^2 = -5$
no real solution

That simply means that there is no point whatsover where the function is undefined.

Therefore the domain of the function is $RR$ .

What is the domain of f(x)=(x+6)/(x^2+5) f(x)=x+6x2+5f(x)=(x+6)/(x^2+5) ?