If and , where is the fractional part of ,…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

f: \mathbb{R} \to \mathbb{R}

and

f(x) = \frac{\sin(\pi\{x\})}{x^4 + 3x^2 + 7}

, where

\{x\}

is the fractional part of

x

, then (1)

f

is injective (2)

f

is not one-one and non-constant (3)

f

is a surjective (4)

f

is a zero function