Determine the range of the function f(x)=x2−4x+3x2+1f(x) = \frac{x^2 - 4x + 3}{x^2 + 1}f(x)=x2+1x2−4x+3.
[−1,5][-1, 5][−1,5]
[1−22,1+22][1-2\sqrt{2}, 1+2\sqrt{2}][1−22,1+22]
(−1,3](-1, 3](−1,3]
[1/2,2][1/2, 2][1/2,2]