Question

Write the domain of the real function $f\left(x\right)=\sqrt{x-\left[x\right]}.$

Answer 1

[x] is the greatest integral function.
$$\begin{gathered} \text{So, 0≤}x-\left[x\right]<1 \\ \Rightarrow \sqrt{x-\left[x\right]}\text{exists for every}x\in R. \\ \text{⇒Domain =}R \end{gathered}$$