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Q.
If { } denotes the fractional part of x, the range of the function $f\left(x\right) = \sqrt{\left\{x\right\}^{2}-2\left\{x\right\}}$ is
Relations and Functions
Solution:
$\left\{x^{2}\right\}-2\left\{x\right\} \ge 0$
$\Rightarrow \left\{x\right\} \left\{x\right\}-2 \ge 0$
$\Rightarrow \left\{x\right\}\le 0$ or $\left\{x\right\} \ge 2$
Second case is not possible.
Hence $\left\{x\right\} = 0$, as $\left\{x\right\}\le [0,\, 1)$. Hence range of $f \left(x\right)$ contains only one element $0.$