For each of the following pairs of functions, either f$($n$)$ is O$($g$($n$)),$ f$($n$)$ is $\backslash$Omega $($g$($n$)),$ or f$($n$)$ is $\backslash$Theta $($g$($n$)).$ Determine which relationship is correct.

$***$Make sure to first find the simplest form of f$($n$),$ then decide which relationship is correct. Note: lg refers to log base $2$

f$($n$)=2$nlg$($n$+2)^(2)+($n$+2)^(2)$ lg$($n$/2)$ ; g$($n$)=$n$^(2)$lg$($n$)$

f$($n$)=2^($n$+1)+3^($n$1)$ ; g$($n$)=3^($n$)$