What is the smallest integer value of $c$ such that the function $f(x)=\frac{x^2+1}{x^2-x+c}$ has a domain of all real numbers?
+2666 For the function to have a domain of all real numbers, the denominator must ave imaginary solutions.
For an equation to have imaginary solutions, the discriminant(b^2 - 4ac) must be negative.
So, we have the equation \(1 - 4c < 0\). The smallest possible integer that works is \(\color{brown}\boxed{1}\)
+2666 For the function to have a domain of all real numbers, the denominator must ave imaginary solutions.
For an equation to have imaginary solutions, the discriminant(b^2 - 4ac) must be negative.
So, we have the equation \(1 - 4c < 0\). The smallest possible integer that works is \(\color{brown}\boxed{1}\)
