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

1 Answer
Sep 7, 2015

Answer:

The domain of the function is #RR#.

Explanation:

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#.