Given the list of functions $f$($n$)$$ and $g$($n$)$$ below, use the "most precise" asymptotic notation to show how function $f$ is related to function $g$ in each case $($i$.$e$.,$ $f$($n$)\backslash$in O$($g$($n$)),$ f$($n$)\backslash$in $\backslash$Omega$($g$($n$))$$$,$ or $f$($n$)\backslash$in $\backslash$Theta$($g$($n$))$$$.$ For example, if $f$($n$)=$n$ and $g$($n$)=2$ n$+1$$ then the correct answer is $f$($n$)\backslash$in $\backslash$Theta$($g$($n$))$$$.$ Assume logarithms are base $2$ unless stated otherwise.