Suppose the Laplace transform of ft is given by s2 5s 33s

Suppose the Laplace transform of f(t) is given by s^2 - 5s - 3/(3s + 1)(2s - 1) find the Laplace transform of f L(f(41)) = You have not attempted this yet

Solution

Given that L(f(t)) = (s²-5s-3)÷(3s+1)(2s-1)²

We know that L(f(t)) = (s)

then L(f(at)) = (s/a)÷a

implies L(f(4t)) = (s/4)÷4

= [(s/4)²-5(s/4)-3)]÷4[((3s/4)+1)((2s/4)-1)²]

= 16[s²-20s-48]÷4(16)[(3s+4)(s²+4-4s)]

= (s²-20s-48)÷4(3s+4)(s²+4-4s)