Functions

Geometry Level 3

Let \(f(x)=\sqrt { \sin(\pi x/2) } +\sqrt { 16-{ x }^{ 2 } } +\sqrt { x } +\log _{ 2 }{ { (x }^{ 2 } } -2x)\).

If p be the sum of all possible integers in the domain of f(x) and q be the sum of all possible integers in the range of f(x), then

\(4\left[ \frac { q }{ p } \right] -4\left\{ \frac { q }{ p } \right\} \) is equal to ?

Note : [.] denotes greatest integer function and {.} denotes fractional part function.

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