Piece wise function and Laplace Transform

[brad sue]

Hi,
I need to find the piece wise function whose the the Laplace Transform is:

2/s+e^-3x(1/s²)+4e^-3x(1/s)

I found for f as function of the unit step function u:
f(x)=2+x*u(x-3)+u(x-3)

Now I have difficulty to put the function in piece wise form like:

f(x)= 2 for 0<x<2 and f(x)=... for x>3

How can I found the expression of f(x) for x>3??

Thank you
B

 

[FrogPad]

The definition of the heaviside unit step function is:

$$U(t-t_0) = \left[ \begin{array}{c}1\,\,t\geq t_0 \\ 0\,\,t<t_0 \end{array}$$

right?

so:

first factor your function:
$$f(x)=2+x*u(x-3)+u(x-3)$$

$$f(x) = 2+u(x-3)(x+1)$$
Now plug in the definition of the function:$$f(x)=2+(1)(x+1) \,\,\,t \geq 3$$
$$f(x)=2+(0)(x+1) \,\,\,t < 3$$

does that makes sense?