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The domain of the function $f (x) = \sqrt{x^{2} - [x]^{2}},$ where [x] is the greatest integer less than or equal to x, is

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$[0, + \infty)$

none of these

$(- \infty, 0]$

answer is D.

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Detailed Solution

$x^{2} - [x]^{2} \geq 0 or x^{2} \geq [x]^{2}$

This is true for all positive values of x and all negative integers x.

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