How do you find the domain of this rational function: #G(x) = (x-3)/(x^4+1)#?

1 Answer
Apr 12, 2015

As this is a rational function we want to be sure that the denominator is diferent from zero, but in this case the denominator will never become zero regardless of the value (real) of #x#. In fact, even if you choose a negative #x# the #4# power will change it into positive that will add to 1 to give a value diferent from zero!
So the domain is all the real #x#.

graph{(x-3)/(x^4+1) [-10, 10, -5, 5]}