$($a$)$ Find the function f$($t$)$f$($t$)$ such that L$[$f$($t$)]=4$se$2$s$2$s$2+8$L$[$f$($t$)]=4$se$2$s$2$s$2+8.$f$($t$)=$f$($t$)=$

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$($b$)$ Find the function g$($t$)$g$($t$)$ such that L$[$g$($t$)]=4$e$3$s$5$s$2+80$L$[$g$($t$)]=4$e$3$s$5$s$2+80.$