$($a$)$ Find the function f$($t$)$f$($t$)$ such that L$[$f$($t$)]=53($s$+3)2+75$L$[$f$($t$)]=53($s$+3)2+75.$f$($t$)=$f$($t$)=$

functions

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$($b$)$ Find the function g$($t$)$g$($t$)$ such that L$[$g$($t$)]=4($s$1)3($s$+1)2+27$L$[$g$($t$)]=4($s$1)3($s$+1)2+27.$g$($t$)=$g$($t$)=$

functions

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Note: If you need the step function at t$=$ct$=$c$,$ it should be entered as u$($t$$c$)$u$($t$$c$).$