Let f be a function defined on

$[0,$ $).$

Then the function F defined by

F$($s$)=$

e$$stf$($t$)$ dt$0$

is said to be the Laplace transform of f$.$ The domain of

F$($s$)$

is the set of values of s for which the given improper integral converges.

Use the definition of a Laplace transform to find

$\{$f$($t$)\}.$

$($Write your answer as a function of s$.)$

f$($t$)=$ et $+7$

$\{$f$($t$)\}=$

$($s$>1)$