Which of the following functions have their range equal to (the set of real numbers)?

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Which of the following functions have their range equal to

R

(the set of real numbers)? (1)

x \sin x

(2)

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

, where

[ \cdot ]

denotes the greatest integer function (3)

\frac{x}{\sin x}

(4)

[x] + \{x\}

, where

[ \cdot ]

and

\{ \cdot \}

, respectively denote the greatest integer and fractional part functions