# Solution: 2013-21 Unique inverse

Let $$f(z) = z + e^{-z}$$. Prove that, for any real number $$\lambda > 1$$, there exists a unique $$w \in H = \{ z \in \mathbb{C} : \text{Re } z > 0 \}$$ such that $$f(w) = \lambda$$.

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