# f(x):I will wait for none

Algebra Level 5

Let $$f:(-1,∞)→(-1,∞)$$ be a function satisfying

a)$$\frac{f(x)}{x}$$ is increasing in each of the intervals $$(-1,0)$$ and $$(0,∞)$$.

b)$$f(x+f(y)+xf(y))=y+f(x)+yf(x)$$ for all reals $$x,y$$ in $$(-1,∞)$$

Find the sum of all possible values of $$\sum_{x=0}^{∞}((f(x))^{4}-4\frac{f(x)}{x}-1)$$

Give the answer to 4 decimal places

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