consider the following three functions:

f$($n$)=2^$n $*($log n$)^3$ g$($n$)=$ n$^2*2^($log n$)$ h$($n$)=$ n$^($log n$)*($log n$)!$

which of the following statements is true a out the asymptotic relationships between these functions?

f$($n$)$ is O$($g$($n$))$ and g$($n$)$ is o$($h$($n$))$ but f$($n$)$ is not o$($h$($n$))$

g$($n$)$ is omega$($f$($n$))$ and h$($n$)$