What is the domain of #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#.