$1.[15$ pts$]$ Indicate whether f$($n$)$ is O$($g$($n$)),($g$($n$)),$ or in case it is both, $($g$($n$))\mathrm{.}8\mathrm{.}9.10.11.12.13.14.15.$n$2$n n$0\mathrm{.}110$ log n log$2$ n$($log n$)$log n $2$n n$100$f $($n$)$ n$1/2$g$($n$)$ n$2/31\mathrm{.}2\mathrm{.}3\mathrm{.}4\mathrm{.}5\mathrm{.}6\mathrm{.}7\mathrm{.}2$n $3$n$100$n$+$logn n log nn$+$log$2$ nn$1\mathrm{.}01($log n$)$log nn log$2$ nnlog$2$ n $3$nlog$10$ nlog$($n$2)$log$($n$2)2$log$2$ n$2$n$+1(1\mathrm{.}01)$n