May the floor function help you!

Algebra Level 4

Is \(f(x)\)\(=\)\((-1)^{\lfloor x \rfloor} \sqrt{\frac{1}{4}-(x-\frac{1}{2}-\lfloor x \rfloor)^2}\) an odd or even function?

Try not to use graph!

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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