# Bizarre function

Algebra Level 5

Let $$f:\mathbb{R}^{+} \to \mathbb{R}$$ be a function such that

• $$f$$ is strictly increasing
• $$f(x) > - \dfrac{1}{x} \quad \forall x>0$$
• $$f(x) f \left(f(x)+\dfrac 1x \right) = 1 \quad \forall x>0$$

Find the sum of all possible values of $$f(1)$$.