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?
If it has a domain of all real numbers, then x^2-x+c is never 0.
If you draw out the parabola, x^2-x=y, then you find that the very end is at y=-1/4.
So C must be greater than 1/4, and the smallest integer that works for that is 1.
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