(a) Find the function

f

such that

L[f(t)]=(2)/(3(s+2)^(2)+12)

.\

f(t)=(1)/(3)e

\ (b) Find the function

g

such that

L[g(t)]=(2(s-1))/(4(s+1)^(2)+100)

.\

g(t)=(1)/(2)exp(-t)cos(5t)-(1)/(10)exp(-t)sin(5t)

\ Note: If you need the step function at

t=c

, it should be entered as

u(t-c)

.

(a) Find the function f such that L[f(t)]=3(s+2)2+122. f(t) (b) Find the function g such that L[g(t)]=4(s+1)2+1002(s1). g(t)= Note: If you need the step function at t=c, it should be entered as u(tc)