Find the Domain and Range of the Function
Question:
Write the domain and range of
\[ f(x)=\sqrt{x-[x]} \]
Solution:
Since
\[ 0\le x-[x]<1 \]
therefore
\[ x-[x]\ge0 \]
Hence square root is defined for all real \(x\).
Domain:
\[ \boxed{R} \]
Also,
\[ 0\le x-[x]<1 \]
Taking square root,
\[ 0\le \sqrt{x-[x]}<1 \]
Therefore, range is
\[ \boxed{[0,1)} \]