Let for , where .…

MATHEMATICS · Multi correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

g(x)=\sqrt{x-2k}

for

2k\leq x<2(k+1)

, where

k\in\mathbb{Z}

. Then: (1)

g(x)=\sqrt{x+2}

-2\leq x<0

(2)

g(x)=\sqrt{x-2}

2\leq x<4

(3)

g(x)=\sqrt{x}

0\leq x<2

(4) The period of

g(x)

2