Question

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

Answer 1

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]}