设连续型随机变量 $X$ 的分布函数为 $F(x)$ ，且 $F(0)=0$ ，则下列函数可作为分布函数的是
A
$G_1(x)=\left\{\begin{array}{cc}1+F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$
B
$G_2(x)=\left\{\begin{array}{cc}1-F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$
C
$G_3(x)=\left\{\begin{array}{cc}F(x)+F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$
D
$G_4(x)=\left\{\begin{array}{cc}F(x)-F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$
E
F