The domain of the function $f(x) = \frac{1}{1 + e^x}$ is $[-1, 1]$. Find the range of the function.
- A$\left( \frac{1}{1+e}, \frac{1}{1+e^{-1}} \right)$
- B$[-1, 0]$
- C$[0, 1]$
- D$[-1, 1]$
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