Let and , where denotes fractional part…

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

f(x) = x - x^2

and

g(x) = \{x\}

\forall x \in R

where

\{ \}

denotes fractional part function. (1) Statement I

f(g(x))

will be continuous,

\forall x \in R

. (2) Statement II

f(0) = f(1)

and

g(x)

is periodic with period 1.