# Another JEE Mains problem

Algebra Level 5

$\large {f(x)=\frac{1}{\sqrt{\{x+1\}-x^{2}+2x}}}$

If the domain of $$f(x)$$ above, where $$\{x+1\}$$ denotes the fractional part of $$x+1$$, can be expressed as $$\left(\dfrac{a-\sqrt{b}}{c},c \right)\backslash \{d\}$$, where $$a$$, $$b$$, $$c$$, and $$d$$ are coprime integers and $$\backslash \{d\}$$ denotes excluding the value $$d$$, find $$a+b+c+d$$.

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