Funky Function

Algebra Level 5

Let f(x) f(x) be a real valued function defined on xR,x0,1 x \in \mathbb{R}, x\neq 0, 1 such that for all real values of xx, f(x)+f(x1x)=1x. f(x) + f\left( \frac {x-1} {x} \right) = \frac{1}{x}. f(4)=ab f(-4) = \frac {a} {b} , where a a and bb are coprime integers. What is a+b a + b ?

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