What is the smallest integer value of c such that the function f(x) = (x^2 + 1)/(x^2 + 1 + c) has a domain of all real numbers?
+2666 Note that the function will not have a domain of all real numbers when the denominator has a real solution for x.
This means we are looking for the smallest number where the roots of \(x^2 +1 + c = 0\) are imaginary.
The smallest number in which this is satisfied is \(\color{brown}\boxed{0}\)
