Inverse of Absolute Value Function

Algebra Level 3

Consider the function \( f: [ -1, \infty) \rightarrow \mathbb{R} \), given by \(f(x)=|x+1|+1\).

Which of the following must be in the domain of the inverse function \(f^{-1}(x)\)?

I: \(-1\).
II: \(0\).
III: \(1\).

\[\] Notation: \( | \cdot | \) denotes the absolute value function.

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