In the following, f$($x$),$ g$($x$)$ and h$($x$)$ are all positive value real functions.

$($Note: Answer true if for any possible positive value real function f$($x$)$ g$($x$)$ and h$($x$),$ the statement is true. If a counter example of f$,$ g$,$ and h can make the statement false, then it is false.$)$

If f$($x$)$ is O$($g$($x$)),$ then $2$f$($x$)$ belongs to O$($g$($x$))$

If f$($x$)$ is O$($g$($x$)),$ g$($x$)$ is $\backslash$Theta $($h$($x$)),$ then f$($x$)$ belongs to O$($h$($x$))$

If f$($x$)$ and g$($x$)$ are O$($n$^2),$ then f$($x$)+$g$($x$)$ belongs to O$($n$^2)$

If f$($x$)$ and g$($x$)$ are O$($n$^2),$ then f$($x$)-$g$($x$)$ belongs to O$($n$^2)$

If f$($x$)$ is O$($g$($x$)),$ and g$($x$)$ is O$($n$),$ then f$($x$)+$g$($x$)$ belongs to O$($n$)$