T/F (feat.symmetry)

Which of the following is ALWAYS true? Note: $f,g,h$ are real-valued functions defined in all reals.

1. $f(x)$ can be expressed as a sum of two functions $f_1(x)$ and $f_2(x)$ , where $\forall x, f_1(-x)=f_1(x), f_2(-x)=-f_2(x)$

2. Consider $g(x),h(x)$ which are both symmetrical ( line symmetry ) and periodic (period of both functions need not be the same). There exists some $c$ such that $g(c)=h(c)$ . Let $a$ be the $y$ value of the intersection point(s) of $y= g(x), y=h(x)$ . Denote $P=\{ x|g(x)=a \}$ , $Q=\{ x|h(x)=a \}$ .

Given that $P \subset Q$ or $Q \subset P$ , there exists some $m$ such that, $\forall x,g(2m-x)=g(x), h(2m-x)=h(x)$

3. Given that $\frac{d}{dx}i(x)=\frac1{x}$ for all non-zero $x$ , $i(-x)=i(x)$