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Question
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Solution
\[\text{ We know that } \]
\[[x] - x = - {x}, \text{ which is the fractional part of any real number x } . \]
\[\text{ Thus } , f(x) = \sqrt{- {x}} . \]
\[\text{ Since {x} is always a positive number, f(x) is not defined for any x . } \]
\[\text{ Or dom } (f) = \varphi\]
\[\text{ Thus, range } (f) = \varphi . \]
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