Find the Domain of \(f(x)=x+[x]\)
Question
Find the domain of the function
\[ f(x)=x+[x] \]where \([x]\) denotes the greatest integer function.
Solution
Given
\[ f(x)=x+[x] \]The function \(x\) is defined for all real numbers.
Also, the greatest integer function \([x]\) is defined for every real number \(x\).
Therefore, the sum
\[ x+[x] \]is defined for all real numbers.