First slide

Functions (XII)

Question

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

Moderate

A

$\begin{array}{l} R \end{array}$
B

$\begin{array}{l} [0, + \infty) \end{array}$
C

$(- \infty, 0]$
D

None of these

Solution

$x^{2} - {[x]}^{2} \geq 0 or x^{2} \geq {[x]}^{2}$
This is true for all non-negative values of x and all negative
integers x.

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