Answer
All real numbers
Work Step by Step
The domain of the function is all real numbers, except for when the denominator is 0. Thus, we let the denominator equal 0:
$$x^4 +1 =0 \\ x= \sqrt [4] {-1} $$
We can never take the fourth root of a negative number. Thus, the denominator will never equal 0, meaning that the function will exist for all real numbers.
