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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