Consider the functions | Condition | | |---|---| | | | | | | and

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

Problem

Consider the functions

Condition	$f(x)$
$-1 \le x \le 0$	$x - 1$
$0 \le x \le 1$	$x^2$

and

g(x) = \sin x

. If

h_1(x) = f(|g(x)|)

and

h_2(x) = |f(g(x))|

, which of the following is not true about

h_2(x)

? (1) The domain is

\mathbb{R}

(2) It is periodic with period

2\pi

(3) The range is

[0,1]

(4) None of the above