Mathematics

Problem

Which of the following functions have their range equal to

R

(the set of real numbers)? a.

x \sin x

\frac{[x]}{\tan 2x} \cdot x \in \left(-\frac{\pi}{4}, \frac{\pi}{4}\right) - \{0\}

, where

[ \cdot ]

denotes the greatest integer function c.

\frac{x}{\sin x}

[x] + \{x\}

, where

[ \cdot ]

and

\{ \cdot \}

, respectively denote the greatest integer and fractional part functions