Determine the range of f(x)=x2+1x2+2f(x) = \frac{x^2+1}{x^2+2}f(x)=x2+2x2+1 for all x∈Rx \in \mathbb{R}x∈R.
[0,1)[0, 1)[0,1)
(0,1/2](0, 1/2](0,1/2]
[1/2,1)[1/2, 1)[1/2,1)
(1/2,1](1/2, 1](1/2,1]