Recall the "Big$-$O$"-$notation.

If f and g are functions then f$($n$)$ in O$($g$($n$))$f$($n$)$ in O$($g$($n$))$ if there is a constant c$>0$c$>0$ such that f$($n$)$cg$($n$)$f$($n$)$cg$($n$)$ for all sufficiently large values of n$.$

We write f$($n$)$ in $($g$($n$))$f$($n$)$ in $($g$($n$))$ if$$ both f$($n$)$ in O$($g$($n$))$f$($n$)$ in O$($g$($n$))$ and g$($n$)$ in O$($f$($n$))$g$($n$)$ in O$($f$($n$)).$

Question $6$Select one or more:

a$.$

$17$n$3$ in $($n$3)17$n$3$ in $($n$3)$

b$.$

n$2$ in O$($nlog$($n$))$n$2$ in O$($nlog$($n$))$

c$.$

n$!$ in O$(2$n$)$n$!$ in O$(2$n$)$

d$.$

nlog$($n$)$ in O$($n$2)$nlog$($n$)$ in O$($n$2)$

e$.$

$10000$n$10000$ in O$(1\mathrm{.}001$n$)10000$n$10000$ in O$(1\mathrm{.}001$n$)$

f$.$

n$1000$ in O$(2$n$)$n$1000$ in O$(2$n$)$

g$.$

log$($n$)$ in O$(1)$log$($n$)$ in O$(1)($Here $"1"$ denotes the function f$($n$)=1$f$($n$)=1$ for all natural numbers nn$).$

h$.$

n$5$ in O$($n$4)$