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## Homework Statement

is it possible to find the laplace transform of f(t-b) ? i don't know if its possible, i am just trying.

## The Attempt at a Solution

so, where integral from 0 to infinity,

[itex]\int[/itex] f(t-b) e

^{-st}dt

let t-b = z

=[itex]\int[/itex]f(z) e

^{-s(z+b)}dz

=[itex]\int[/itex]f(z) e

^{-sz}e

^{-sb}dz

=e

^{-sb}f(s) , where f(s) is the laplace transform?

if this is correct, then

**is f(s) the laplace transform of f(z)? i.e of f(t-b) ?**

__question)__**is it the laplace transform of f(t) only?**

__OR__because, from above, the expressions are telling me that f(s) is the laplace transform of f(z) which is f(t-b)

but if that is the case, then it wouldn't make any sense to even compute the laplace transform by the above method. because it would then mean L { f(t-b) } = f (s) ?

if the entire above is wrong, then how do i compute it?

because i know the inverse laplace transform of e

^{-bs}f(s) is f(t-b), so the reverse has to be true